Every measurement or calculation we do with instruments in chemistry has some level of uncertainty called *experimental error*. Significant figures are necessary to communicate a level of accuracy and precision while dealing with this uncertainty.

**Rules for Number of Signficant Figures**

__Rule 1__: If your number has a ** decimal point** move from

*Trailing zeros* are a sequence of zeros after the decimal point once you’ve passed all non-zero integers. They would be significant.

__Rule 2: __If your number has ** NO decimal point** move from

If a value has no decimal point then the final zero would mean it has an infinite number of significant figures.

**Exact Numbers **

Exact numbers contain an infinite number of significant figures because they represent the amount of a particular item and not a measurement.

For example, when we say that a decade is equal to 10 years, there are 150 students in your chemistry class, or NH_{3} contains 1 atom of nitrogen and 3 atoms of hydrogen.

**Addition & Subtraction**

When dealing with addition or subtraction the least number of decimal places will determine the final answer.

^{6}, but the final answer should have only 1 decimal place and so the answer is rounded. Adding the two values gives the initial value of 5.375 x 10

**Multiplication & Division**

When dealing with multiplication or division the least number of significant figures will determine the final answer.

Multiplying the two values gives an initial value of 103.6, but you must round your final answer to significant figures.

Furthermore keep in mind when dealing with mixed operations we must follow the same arithmetic guidelines as we always do.

**Logarithm & Natural Logarithm**

When taking the (log) or (ln) of a value, the number of significant figures it has determines the number of digits ** after** the decimal point for the answer.

Using your calculator, the log of 1.53 x 10^{-3} gives an initial value of - 2.01531. The value of 1.53 x 10^{-3} has 3 significant figures and so the final answer should have 3 digits after the decimal point.

While standing on the summit, you discover there are 16 other people on the top of Africa with you. This number of people has how many significant digits?
A) 1
B) 2
C) 3
D) 4
E) unlimited

Give the correct number of significant figures for the following computation:
a) 1
b) 2
c) 3
d) 4
e) 5

How many significant figures are in the measurement, 20.300 m?
A) 3
B) 4
C) 5
D) 1
E) 2

Read each measurement to the correct number of significant figures. Note: Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

Read each measurement to the correct number of significant figures. Note: Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

Read each measurement to the correct number of significant figures. Note: Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

How many significant figures are in each number?
a. 0.000312 m
b. 312,000 s
c. 3.12 X 105 km
d. 13,127 s
e. 2000

What is the value for y, rounded correctly and to the proper number of significant figures when x = 0.320 in the following equation?
y = 7.3562 x - 0.14
a. 2.2
b. 2.214
c. 2.2140
d. 2.21
e. 2.2138

Indicate the number of significant figures in each number. If the number is an exact number, indicate an unlimited number of significant figures.
a. 305,435,087 (2008 U.S. population)
b. 2.54 cm = 1 in
c. 11.4 g/ cm3 (density of lead)
d. 12 = 1 dozen

Round each number to four significant figures.
a. 156.182
b. 156.842
c. 156.849
d. 156.899

Consider the addition of 15.4 to 28. What would a mathematician say the answer is? What would a scientist say? Justify the scientist’s answer, not merely citing the rule, but explaining it.

Round each number to three significan t figures.
a. 79,845.82
b. 1.548937 X 107
c. 2.3499999995
d. 0.000045389

Consider multiplying 26.2 by 16.43. What would a mathematician say the answer is? What would a scientist say? Justify the scientist’s answer, not merely citing the rule, but explaining it.

Calculate to the correct number of significant figures.
a. 89.3 X 77.0 X 0.08

Calculate to the correct number of significant figures.
b. (5.01 X 105) ÷ (7.8 X 102)

Calculate to the correct number of significant figures.
c. 4.005 X 74 X 0.007

Calculate to the correct number of significant figures.
d. 453 ÷ 2.031

Calculate to the correct number of significant figures.
a. 43.7 - 2.341

Calculate to the correct number of significant figures.
b. 17.6 + 2.838 + 2.3 + 110.77

Calculate to the correct number of significant figures.
c. 19.6 + 58.33 - 4.974

Calculate to the correct number of significant figures.
d. 5.99 - 5.572

Calculate to the correct number of significant figures.
a. [( 1.7 X 106) ÷ (2.63 X 105)] + 7.33

Calculate the following to the correct number of significant figures.
a) 2
b) 1.5
c) 1.51
d) 1.510
e) 1.5103

Calculate to the correct number of significant figures.
b. (568.99 - 232.1) ÷ 5.3

Calculate to the correct number of significant figures.
d. (3.14 X 2.4367) - 2.34

At 4.000°C water’s density is 1.000 g/cm 3. For the range of temperatures associated with “room temperature” the density of pure water is:
Density (g/cm 3) = (-0.00030 (g/°C • cm 3) x Temperature (°C) + 1.0042 (g/cm 3)
Based on this thermometer reading, how many significant figures should you report for the calculated density?
a) One b) Two c) Three d) Four e) Five

Calculate to the correct number of significant figures.
c. (9443 + 45 - 9.9) X 8.1 X 106

Perform the following calculation to the right number of sig figs:
a) 1
b) 2
c) 3
d) 4

Which of the following numbers has the greatest number of significant figures?
A. 1.500 B. 2.4 x 10 4 C. 0.00085 D. 752,000

What is the correctly reported mass of water based on this data?
(A) 1.3 g
(B) 1.30 g
(C) 1.298 g
(D) 1.2980 g

How many significant figures are in the following?
6.022 x 1023 =
340384 =
10.00 =
8.1000 =
0.00000000003 =

There are 6 significant figures in the number 0.003720.
A. True
B. False

Read the water level with the correct number of significant figures.
A) 5 mL
B) 5.4 mL
C) 5.42 mL
D) 5.420 mL
E) 5.4200 mL

Give the answer with correct significant figures.
4.56 / (7.49 + 5.493 - 5.345)

How many significant figures are in 1009.630 mL?
A) 3
B) 4
C) 5
D) 6
E) 7

What answer should be reported, with the correct number of significant figures, for the following calculation?
(965.43 × 3.911) + 9413.4136
A) 13189
B) 13189.2
C) 1.32 × 104
D) 1.3 × 104
E) 1.319 × 104

Do each calculation without using your calculator and give the answers to the correct number of significant figures.
1.76 X 10- 3 / 8.0 X 102

Do each calculation without using your calculator and give the answers to the correct number of significant figures.
b. 1.87 X 10- 2 + 2 X 10- 4 - 3.0 X 10-3

Do each calculation without using your calculator and give the answers to the correct number of significant figures.
[(1.36 X 105)(0.000322)/ 0.082](129.2)

You weigh an object on a balance and read the mass in grams according to the picture. How many significant figures are in this measurement?

How many significant figures are in each of the following measurements?35.0445 g

How many significant figures are in each of the following measurements?59.0001 cm

How many significant figures are in each of the following measurements?0.03003 kg

How many significant figures are in each of the following measurements?0.00450 m

How many significant figures are in each of the following measurements?67,000 m2

The following statements are all true.
a.
Jessicas house is 5 km from the grocery store.
b.
Jessicas house is 4.73 km from the grocery store.
c.
Jessicas house is 4.73297 km from the grocery store.What does the number of digits in each statement communicate?

What is the number of significant figures in each of the following measured quantities?601 kg

How many significant figures are in each number?1,050,501
km

What is the number of significant figures in each of the following measured quantities?0.054 s

How many significant figures are in each number?0.00020
m

What is the number of significant figures in each of the following measured quantities?6.3050 cm

How many significant figures are in each number?0.005710
s

What is the number of significant figures in each of the following measured quantities?0.0105 L

How many significant figures are in each number?0.001090
cm

How many significant figures are in each number?180,701
mi

What is the number of significant figures in each of the following measured quantities?400 g

How many significant figures are in each number?0.01040
m

How many significant figures are in each number?0.005710
km

How many significant figures are in each number?90,201
m

How many significant figures are in each of the following numbers?0.000312 m

How many significant figures are in each of the following numbers?312,000 s

How many significant figures are in each of the following numbers?3.12 105

How many significant figures are in each of the following numbers?13,127 s

How many significant figures are in each of the following numbers?2000

Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?= 3.14

Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?12 inches = 1 foot

Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?EPA gas mileage rating of 26 miles per gallon

Which of the following numbers are exact numbers and therefore have an unlimited number of significant figures?1 gross = 144

Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.284,796,887 (2001 U.S. population)

Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.2.54 cm = 1 in

Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.11.4 g/cm3 (density of lead)

Indicate the number of significant figures in each of the following numbers. If the number is an exact number, indicate an unlimited number of significant figures.12 = 1 dozen

How many significant figures does each of the following quantities have?76.600
kJ

How many significant figures does each of the following quantities have?3000 nm

How many significant figures does each of the following quantities have?0.00300
mL

How many significant figures does each of the following quantities have?18 students

A temperature measurement of 25oC has three significant figures, while a temperature measurement of -196oC has only two significant figures.Explain.

How many significant figures does each of the following quantities have?47.60
mL

How many significant figures does each of the following quantities have?2070 mi

Is the use of significant figures in each of the following statements appropriate?On July 1, 2005, the population of Cook County, Illinois, was 5,303,683.

Is the use of significant figures in each of the following statements appropriate?In the United States, 0.621
% of the population has the surname Jones.

Is the use of significant figures in each of the following statements appropriate?You calculate your grade point average to be 3.87532.

A sample that has a mass of about 25 g is weighed on a balance that has a precision of 0.1 g. How many significant figures should be reported for this measurement?

Perform the following calculations to the correct number of significant
figures.(86.6 - 23.501) 0.0051

Perform the following calculations to the correct number of significant
figures.[(2.51106) 47.501] + 145.01

Perform the following calculations to the correct number of significant
figures.[(1.8106) (2.66105)] + 7.51

Perform the following calculations to the correct number of significant
figures.(550.01 - 225.1) 5.4

Perform the following calculations to the correct number of significant
figures.(9453 + 47 - 7.5) (8.3106)

What is the temperature reading on the Celsius thermometer? (The perspective is not technically ideal, readings should be done at eye-level with the meniscus.)

How many milliliters of water does the graduated cylinder in (a) contain?

How tall in centimeters is the paper clip in (b)?

An oven thermometer with a circular scale reading degrees Fahrenheit is shown. What temperature does the scale indicate?

Read each of the following to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus.

Read each of the following to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus.

Read each of the following to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus.

Read the volume of the cylinder and report your answer to the correct number of significant figures.
The volume is indicated by the bottom of the meniscus.

The diameter of Earth at the equator is 7926.381 mi. Round this number to three significant figures, and express it in standard exponential notation.

The circumference of Earth through the poles is 40,008 km. Round this number to four significant figures, and express it in standard exponential notation.

What is the following number to four significant figures in standard exponential notation: 656,980

What is the following number to four significant figures in standard exponential notation: 0.008543210

What is the following number to four significant figures in standard exponential notation: 0.000257870

What is the following number to four significant figures in standard exponential notation: -0.0357202

What are the rules for rounding off the results of calculations?

The diameter of Jupiter at its equator is
142984 km.Round off this quantity to four significant figures.

The diameter of Jupiter at its equator is
142984 km.Round off this quantity to two significant figures.

Round off the following quantities to the number of significant figures indicated in parentheses.3.567006×104 m (4)

Round off the following quantities to the number of significant figures indicated in parentheses.70.427 g (2)

The following statements are all true.
a.
Jessicas house is 5 km from the grocery store.
b.
Jessicas house is 4.73 km from the grocery store.
c.
Jessicas house is 4.73297 km from the grocery store.How can all the statements be true?

Round off the following quantities to the number of significant figures indicated in parentheses.4936 cm (3)

Round off the following quantities to the number of significant figures indicated in parentheses.2.30003×10−4 kg (5)

Round off the following quantities to the number of significant figures indicated in parentheses.3.567006×104 m (6)

Round off the following quantities to the number of significant figures indicated in parentheses.70.427 g (3)

Round off the following quantities to the number of significant figures indicated in parentheses.6.5004 kg (4)

Round off the following quantities to the number of significant figures indicated in parentheses.1.904 km (3)

Round off the following quantities to the number of significant figures indicated in parentheses.13.0004 g/cm3 (3)

Round off the following quantities to the number of significant figures indicated in parentheses.2.2500004×106 (7)

Round each of the following numbers to four significant figures.155.052

Round each of the following numbers to four significant figures.155.042

Round each of the following numbers to four significant figures.155.049

Round each of the following numbers to four significant figures.155.099

When multiplying or dividing measured quantities, what determines the number of significant figures in the result?

Perform the following calculations to the correct number of significant
figures.(2.210106) (7.1104)

Do each calculation and give the answers to the correct number of significant figures.1.7610-3/8.1102

Do each calculation and give the answers to the correct number of significant figures.[(1.35105)(0.000351)/0.083](122.1)

When adding or subtracting measured quantities, what determines the number of decimal places in the result?

Carry out the following calculations, expressing each result with
the correct number of significant figures:24.567 g + 0.044 78 g = ? g

Carry out the following calculations, expressing each result with
the correct number of significant figures:0.378 mL + 42.3 mL - 1.5833 mL = ? mL

The diameter of Earth at the equator is 7926.381 mi. Round this number to three significant figures, and express it in standard exponential notation.

Carry out the following operations, and express the answers with the appropriate number of significant figures.(a) 12.0550 + 9.05

What is the number of significant figures in each of the following measured quantities?(a) 358 kg

What is the number of significant figures in each of the following measured quantities?(b) 0.054 s

What is the number of significant figures in each of the following measured quantities?(c) 6.3050 cm

What is the number of significant figures in each of the following measured quantities?(d) 0.0105 L

What is the number of significant figures in each of the following measured quantities?(e) 7.0500 x 10–3m3

Indicate the number of significant figures in each of the following measured quantities:(a) 3.774 km

Indicate the number of significant figures in each of the following measured quantities: (b) 205 m2

Indicate the number of significant figures in each of the following measured quantities: (c) 1.700 cm

Indicate the number of significant figures in each of the following measured quantities: (e) 307.080 g

Indicate the number of significant figures in each of the following measured quantities: (d) 350.00 K

Carry out the following operations, and express the answers with the appropriate number of significant figures.(b) 257.2 - 19.789

Carry out the following operations, and express the answers with the appropriate number of significant figures.(e) (6.21 x 103) (0.1050)

Carry out the following operations, and express the answers with the appropriate number of significant figures.(d) 0.0577/ 0.753

Carry out the following operations, and express the answer with the appropriate number of significant figures.(a) 320.5 - (6104.5/2.3)

Carry out the following operations, and express the answer with the appropriate number of significant figures.(b) [(285.3 x 105) – (1.200 x 103)] x 2.8954

Carry out the following operations, and express the answer with the appropriate number of significant figures.(c) (0.0045 x 20,000.0) + (2813 x 12)

Solve and give the correct number of significant figures to the problem below.5.80 x 10 –1 – 3.4 x 10 –2 =A) 5.5 x 10 –2B) 2.4 x 10 2C) 5.46 x 10 –1D) 2.4 x 10 –3E) 5.5 x 10 –1

You weigh an object on a balance and read the mass in grams according to the picture. How many significant figures are in this measurement?

You have a graduated cylinder that contains a liquid (see photograph). Write the volume of the liquid, in milliliters, using the proper number of significant figures.

For each number, underline the zeroes that are significant and draw an x through the zeroes that are not:a. 1,050,501 km b. 0.0020 mc. 0.000000000000002 s d. 0.001090 cm

All 50 students agree that in the classroom there are 100 chairs. This number has:
a. 1 significant figure
b. 2 significant figures
c. 3 significant figures
d. Infinite number of significant figures
e. We cannot know with the available information

How many significant figures are in each of the following?a. 100

How many significant figures are in each of the following?b. 1.0 x 10 2

How many significant figures are in each of the following?c. 1.0 x 10 3

How many significant figures are in each of the following?d. 100.

How many significant figures are in each of the following?e. 0.0048

How many significant figures are in each of the following?f. 0.00480

How many significant figures are in each of the following?g. 4.80 x 10–3

How many significant figures are in each of the following?g. 4.800 x 10–3

Evaluate each of the following and write the answer to the appropriate number of significant figures.a. 212.2 + 26.7 + 402.09

Evaluate each of the following and write the answer to the appropriate number of significant figures.b. 1.0028 + 0.221 + 0.10337

Evaluate each of the following and write the answer to the appropriate number of significant figures.c. 52.331 + 26.01 - 0.9981

(a) What is the length of the pencil in the following figure if the scale reads in centimeters? How many significant figures are there in this measurement?

Evaluate each of the following and write the answer to the appropriate number of significant figures.d. 2.01 x 102 + 3.014 x 103

(b) An oven thermometer with a circular scale reading degrees Fahrenheit is shown. What temperature does the scale indicate? How many significant figures are in the measurement? [Section 1.5]

Evaluate each of the following and write the answer to the appropriate number of significant figures.e. 7.255 - 6.8350

Perform the following mathematical operations, and express each result to the correct number of significant figures.a. 0.102 x 0.0821 x 273 / 1.01

Perform the following mathematical operations, and express each result to the correct number of significant figures.b. 0.14 x 6.022 x 10 23

Perform the following mathematical operations, and express each result to the correct number of significant figures.c. 4.0 x 10 4 x 5.021 x 10-3 x 7.34993 x 102

(a) How many significant figures should be reported for the volume of the metal bar shown below? [5ection 1.5]

Perform the following mathematical operations, and express each result to the correct number of significant figures.d. 2.00 x 106 / 3.00 x 10 -7

Perform the following mathematical operations and express the result to the correct number of significant figures.a. 2.526 / 3.1 + 0.470 / 0.623 + 80.705 / 0.4326

Perform the following mathematical operations and express the result to the correct number of significant figures.b. (6.404 x 2.91) / (18.7 - 17.1)

Perform the following mathematical operations and express the result to the correct number of significant figures.c. 6.071 x 10-5 - 8.2 x 10-6 - 0.521 x 10-4

Perform the following mathematical operations and express the result to the correct number of significant figures.d. (3.8 x 10-12 + 4.0 x 10-13) / (4 x 1012 + 6.3 x 1013)

Perform the following mathematical operations and express the result to the correct number of significant figures.e. 9.5 + 4.1 + 2.8 + 3.175 / 4(Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.)

Perform the following mathematical operations and express the result to the correct number of significant figures.f. 8.925 - 8.905 / 8.925 x 100(This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

The number of significant figures in 0.066900 x 10 -4 isa. 5b. 6c. 7d. 3e. 4

What is the correct answer to the following expression? 4.13 x 10-10 + 7.59 x 10 -12 a. 4.21 x 10-10 b. 4.2 x 10-10 c. 4 x 10-10 d. 4.206 x 10-10 e. 4.2059 x 10-10

Read the length of the metal bar with the correct number of significant figures.A) 20 cmB) 15 cmC) 15.1 cmD) 15.10 cmE) 15.100 cm

How many significant figures should be used to express the value of x?
x = (23.714 + 86.97 - 0.8693) / 31.7400 ?
A) two
B) three
C) four
D) five
E) six

Determine the number of significant figures for the result of the following arithmetic calculations.
(i) (332.41 + 711.59) (ii) (3.00 x 92.11) / 1.250 (iii) [(25.01 x 6.0) + 40.11]
A) 6, 3, 2
B) 4, 3, 3
C) 5, 3, 2
D) 5, 4, 3
E) 5, 3, 4

How many significant figures are contained in each of the following measurements?(c) 86,002 J

How many significant figures are contained in each of the following measurements?(d) 9.740 × 104 m/s

How many significant figures are there in each of the following values?d. 8 x 108

How many significant figures are contained in each of the following measurements?(e) 10.0613 m3

How many significant figures are there in each of the following values?e. 463.8052

How many significant figures are contained in each of the following measurements? (f) 0.17 g/mL

How many significant figures are contained in each of the following measurements?(g) 0.88400 s

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(b) 12 tablets

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(c) 3% hydrogen peroxide

How many significant figures are there in each of the following values?f. 300

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(d) 5.5 ounces

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(e) 473 mL

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(f) 1.75% bismuth

How many significant figures are there in each of the following values?g. 301

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(g) 0.001% phosphoric acid

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(h) 99.80% inert ingredients

How many significant figures are there in each of the following values?h. 300.

How many significant figures are in each of the following numbers?0.1111 s

How many significant figures are in each of the following?a. 100

How many significant figures are in each of the following numbers?0.007 m

How many significant figures are in each of the following numbers?108,700 km

How many significant figures are in each of the following numbers?1.563300 1011

How many significant figures are in each of the following numbers?30,800

How many significant figures are in each of the following?b. 1.0 x 102

How many significant figures are in each of the following?c. 1.00 x 103

How many significant figures are in each of the following?d. 100.

How many significant figures are in each of the following?e. 0.0048

How many significant figures are in each of the following?f. 0.00480

How many significant figures are in each of the following?g. 4.80 x 10-3

How many significant figures are in each of the following?h. 4.800 x 10-3

How many significant figures are in each number?554 km

How many significant figures are in each number?7 pennies

How many significant figures are in each number?1.01 x 105 m

How many significant figures are in each number?0.00099 s

How many significant figures are in each number?1.4500 km

How many significant figures are in each number?21,000 m

Judge the following statement as true or false. If you believe a statement to be false, provide a corrected version.The number 0.0033 has more significant figures than
0.033.

How many significant figures are in each of the following measurements?3.8200 x 103 km

Underline the significant zero(s) in the following number:• 0.041

Underline the significant zero(s) in the following number:• 0.0410

Underline the significant zero(s) in the following number:• 4.0100 x 104

Underline the significant zero(s) in the following number:• 508

Underline the significant zero(s) in the following number:• 5.080 x 103

Underline the significant zero(s) in the following number:• 0.05080

A. What is the length of the pencil in the figure if the scale reads in centimeters?How many significant figures are there in the measurement in part A?

C. An oven thermometer with a circular scale reading degrees Fahrenheit is shown. What temperature does the scale indicate?How many significant figures are in the measurement in part C?

How many significant figures should be reported for the volume of the metal bar shown below?

Indicate the number of significant figures in each of the following measured quantities.3.774 km

Indicate the number of significant figures in each of the following measured quantities.205 m2

Indicate the number of significant figures in each of the following measured quantities.1.700 cm

Indicate the number of significant figures in each of the following measured quantities.350.00 K

Indicate the number of significant figures in each of the following measured quantities.307.080 g

Indicate the number of significant figures in each of the following measured quantities.1.3 m/s 103 {
m m/s}

Indicate which of the following are exact numbers.(a) the mass of a 32-oz can of coffee(b) the number of students in your chemistry class(c) the temperature of the surface of the Sun(d) the mass of a postage stamp(e) the number of milliliters in a cubic meter of water(f) the average height of NBA basketball players

Indicate which of the following are exact numbers.(a) the mass of a 3- by 5-in. index card(b) the number of ounces in a pound(c) the volume of a cup of Seattle’s Best coffee(d) the number of inches in a mile(e) the number of microseconds in a week(f) the number of pages in this book

How many significant figures does each of the following quantities have?4.50200 x 103 g

How many significant figures does each of the following quantities have?3 x 10-5 g

An object is determined to have a mass of 0.01080 g. How many
significant figures are there in this measurement?

Which statements include exact numbers?(a) Angel Falls is 3212 ft high.(b) There are 8 known planets in the Solar System.(c) There are 453.59 g in 1 lb.(d) There are 1000 mm in 1 m.

Which of the following include exact numbers?(a) The speed of light in a vacuum is a physical constant; to six significant figures, it is 2.99792 x 108 m/s.(b) The density of mercury at 25°C is 13.53 g/mL.(c) There are 3600 s in 1 h.(d) In 2016, the United States had 50 states.

Underline the significant zero(s) in the following number:• 0.41

Underline the significant zero(s) in the following number:• 5.08

Indicate the number of significant figures in each of the following:a. This book contains more than 1000 pages.

Indicate the number of significant figures in each of the following:b. b. A mile is about 5300 ft.

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(a) the number of eggs in a basket

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(a) the number of seconds in an hour

Indicate the number of significant figures in each of the following:c. A liter is equivalent to 1.059 qt.

How many significant figures are contained in each of the following measurements?(a) 38.7 g(b) 2 × 1018 m(c) 3,486,002 kg(d) 9.74150 × 10−4 J(e) 0.0613 cm3(f) 17.0 kg(g) 0.01400 g/mL

How many significant figures are contained in each of the following measurements?(a) 53 cm

The following quantities were reported on the labels of commercial products. Determine the number of significant figures in each.(a) 0.0055 g active ingredients

Indicate the number of significant figures in each of the following:d. The population of the United States in 2015 is 3.1 x 102 million.

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(b) the mass of a dozen eggs

Indicate the number of significant figures in each of the following:e. A kilogram is 1000 g.

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(c) the number of gallons of gasoline necessary to fill an automobile gas tank

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(d) the number of cm in 2 m

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(e) the mass of a textbook

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(f) the time required to drive from San Francisco to Kansas City at an average speed of 53 mi/h

Indicate the number of significant figures in each of the following:f. The Boeing 747 cruises at around 600 mi/h.

How many significant figures are there in each of the following values?a. 6.07 x 10-15

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(b) the number of pages in this book

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(c) the number of grams in your weight

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(d) the number of grams in 3 kilograms

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(e) the volume of water you drink in one day

Which of the following is an inexact quantity?(a) the number of people in your chemistry class(b) the mass of a penny(c) the number of grams in a kilogram

Indicate whether each of the following can be determined exactly or must be measured with some degree of uncertainty:(f) the distance from San Francisco to Kansas City

How many significant figures are contained in each of the following measurements?(b) 2 × 1018 m

How many significant figures are there in each of the following values?b. 0.003840

How many significant figures are contained in each of the following measurements?(c) 3,486,002 kg

How many significant figures are contained in each of the following measurements?(d) 9.74150 × 10−4 J

How many significant figures are contained in each of the following measurements?(e) 0.0613 cm3

How many significant figures are contained in each of the following measurements?(f) 17.0 kg

How many significant figures are contained in each of the following measurements?(g) 0.01400 g/mL

How many significant figures are contained in each of the following measurements?(b) 2.05 × 108 m

How many significant figures are there in each of the following values?c. 17.00

Perform the following mathematical operations and express the result to the correct number of significant figures.a.

Perform the following mathematical operations and express the result to the correct number of significant figures.b. (6.404 x 2.91) / (18.7 - 17.1)

Perform the following mathematical operations and express the result to the correct number of significant figures.c. 6.071 x 10-5 - 8.2 x 10-6 - 0.521 x 10-4

Which of these conversion factors has the potential to change the number of significant figures in a calculation?(i) 1000 m = 1 km(ii) 1 mL = 1 cm3(iii) 1 lb = 453.59 g

Perform the following mathematical operations and express the result to the correct number of significant figures.d. (3.8 x 10-12 + 4.0 x 10-13) / (4 x 1012 + 6.3 x 1013)

Perform the following mathematical operations and express the result to the correct number of significant figures.e. (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.)

Perform the following mathematical operations and express the result to the correct number of significant figures.f. (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

Perform the calculations to the correct number of significant figures.2.5110 x imes21.20 ÷ div(44.11 + 1.223)

Perform the calculations to the correct number of significant figures.(12.01 x imes 0.3) + 4.811

Perform the following mathematical operations, and express the result to the correct number of significant figures.c. 1.285 x 10-2 + 1.24 x 10-3 + 1.879 x 10-1

Perform the following mathematical operations, and express the result to the correct number of significant figures.d.

Perform the following mathematical operations, and express the result to the correct number of significant figures.e.

Perform the following mathematical operations, and express the result to the correct number of significant figures.f.

Perform the following calculations and report each answer with the correct number of significant figures.(h)

Carry out the following operations, and express the answer with the appropriate number of significant figures.320.55 - (6105.5/2.6)

Carry out the following calculation, making sure that your answer has the correct number of significant figures:

Perform the following calculations to the correct number of significant
figures.(25.000 x 12.51) + 350.01

Perform the following calculations to the correct number of significant
figures.(552 ÷ 949.6) + 5.51

Perform the following calculations to the correct number of significant
figures.(3.26 x 2.2501) – 2.26

Carry out the calculation, paying special attention to significant figures, rounding, and units (J = joule, the SI unit of energy; mol = mole, the SI unit for amount of substance):

Carry out the following calculation, making sure that your answer has the correct number of significant figures:

Perform the calculation to the correct number of significant figures.(8.02 - 7.60) /3.003

Evaluate each of the following and write the answer to the appropriate number of significant figures.d. 2.01 x 102 + 3.014 x 103

Read each of the following to the correct number of significant figures. Note that laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

Read each of the following to the correct number of significant figures. Note that laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

Read each of the following to the correct number of significant figures. Note that laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

You have a graduated cylinder that contains a liquid.Write the volume of the liquid, in milliliters, using the proper number of significant figures.

Record the temperature on the thermometer shown here to the correct number of digits.

The beakers shown below have different precisions.a. Label the amount of water in each of the three beakers to the correct number of significant figures.

The beakers shown below have different precisions.a. Label the amount of water in each of the three beakers to the correct number of significant figures.b. Is it possible for each of the three beakers to contain the exact same amount of water? If no, why not? If yes, did you report the volumes as the same in part a? Explain.

Which of the following are exact numbers?a. There are 100 cm in 1 m.b. One meter equals 1.094 yards.c. We can use the equation to convert from Celsius to Fahrenheit temperature. Are the numbers and 32 exact or inexact?d. π = 3.1415927.

How long is the metal strip shown below? Be sure to answer with the correct number of significant figures.

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water, and explain your answers (the numbers given are as precise as possible).a. 128.7 mL

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water, and explain your answers (the numbers given are as precise as possible).b. 18 mL

Draw a picture showing the markings (graduations) on glassware that would allow you to make each of the following volume measurements of water, and explain your answers (the numbers given are as precise as possible).a. 128.7 mL b. 18 mL c. 23.45 mLIf you made these measurements for three samples of water and then poured all of the water together in one container, what total volume of water should you report? Support your answer.

Round off each of the following numbers to two significant figures:(a) 0.436

Round off each of the following numbers to two significant figures:(b) 9.000

Round off each of the following numbers to two significant figures:(c) 27.2

Round off each of the following numbers to two significant figures:(d) 135

Round off each of the following numbers to two significant figures:(f) 0.445

Round off each of the following numbers to two significant figures:(e) 1.497 × 10−3

Round each to three significant figures.79850.02

Round each to three significant figures.1.548952×107

Round each to three significant figures.2.34975001

Round each to three significant figures.0.000045419

Round off each of the following numbers to two significant figures:(a) 517

Round off each of the following numbers to two significant figures:(b) 86.3

Round off each of the following numbers to two significant figures:(c) 6.382 × 103

Round off each of the following numbers to two significant figures:(d) 5.0008

Round off each of the following numbers to two significant figures:(e) 22.497

Round off each of the following numbers to two significant figures:(f) 0.885

Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.a. 0.00034159 to three digits

Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.b. 103.351 x 102 to four digits

Round off each of the following numbers to the indicated number of significant digits and write the answer in standard scientific notation.c. 17.9915 to five digits

Round off each of the following numbers to the indicated number of significant digits and write the answer in standardscientific notation.d. 3.365 x 105 to three digits

Use exponential notation to express the number 385,500 toa. one significant figure.

Use exponential notation to express the number 385,500 tob. two significant figures.

Use exponential notation to express the number 385,500 toc. three significant figures.

Use exponential notation to express the number 385,500 tod. five significant figures.

Round off the number to the indicated number of significant figures (sf): 35.8348 (to 4 sf)

Round off each number to the indicated number of significant figures (sf): 22.4555 (to 3 sf)

Round off the number to the indicated number of significant figures (sf): 0.00845 (to 2 sf)

Round off the number to the indicated number of significant figures (sf): 144,000 (to 2 sf)

Round off the number to the indicated number of significant figures (sf): 0.0003554 (to 2 sf)

Round off the number to the indicated number of significant figures (sf): 231.554 (to 4 sf)

Round off each number in the following calculation to one fewer significant figure, and find the answer:

Round off each number in the following calculation to one fewer significant figure, and find the answer:

Carry out the following operations, and express the answers with the appropriate number of significant figures.0.0589 / 0.678

Calculate the following to the correct number of significant figures.87.6 x 77.0 x 0.09

Calculate the following to the correct number of significant figures.(5.01105) (8.2102)

Calculate the following to the correct number of significant figures.4.505 x 77 x 0.009

Calculate the following to the correct number of significant figures.453 ÷ 2.151

Perform the following calculations and report each answer with the correct number of significant figures. (a) 628 × 342

Perform the following calculations and report each answer with the correct number of significant figures.(b) (5.63 × 102 ) × (7.4 × 103 )

Perform the following calculations and report each answer with the correct number of significant figures.(c)

Perform the following calculations and report each answer with the correct number of significant figures.(d) 8119 × 0.000023

Perform the following mathematical operations, and express the result to the correct number of significant figures.a. 6.022 x 1023 x 1.05 x 102

Perform the calculations to the correct number of significant figures.3.45000 x imes9.441 x imes0.0301 ÷div 2.46

Perform the following mathematical operations, and express the result to the correct number of significant figures.b.

Perform the following calculations and report each answer with the correct number of significant figures.(a) 62.8 × 34

Perform the following calculations and report each answer with the correct number of significant figures.(c) 38 × 95 × 1.792

Perform the following calculations and report each answer with the correct number of significant figures.(e)

Carry out the following calculation, making sure that your answer has the correct number of significant figures:

Carry out the following calculation, making sure that your answer has the correct number of significant figures:V = πr 2h, where r = 6.23 cm and h = 4.630 cm

Perform the following calculations to the correct number of significant
figures.9.16 ÷ 4.960

Perform the following calculations to the correct number of significant
figures.1.62 x 0.03050 x 0.66

Perform the following calculations to the correct number of significant
figures.26.6 x 1.80 ÷ 105.01

Carry out the calculation, paying special attention to significant figures, rounding, and units (J = joule, the SI unit of energy; mol = mole, the SI unit for amount of substance):

Carry out the calculation, paying special attention to significant figures, rounding, and units (J = joule, the SI unit of energy; mol = mole, the SI unit for amount of substance):

Carry out the calculation, paying special attention to significant figures, rounding, and units:

Carry out the following calculations, expressing each result with
the correct number of significant figures:4.6742 g / 0.003 71 L = ? g/L

Carry out the calculation, paying special attention to significant figures, rounding, and units:

Carry out the calculation, paying special attention to significant figures, rounding, and units:

Perform the calculation to the correct number of significant figures.(43.999 x 0.00553)/2.003

Perform the following mathematical operations, and express each result to the correct number of significant figures.a.

Perform the following mathematical operations, and express each result to the correct number of significant figures.b. 0.14 x 6.022 x 1023

Perform the following mathematical operations, and express each result to the correct number of significant figures.c. 4.0 x 104 x 5.021 x 10-3 x 7.34993 x 102

Perform the following mathematical operations, and express each result to the correct number of significant figures.d.

The beakers shown below have different precisions.c. Suppose you pour the water from these three beakers into one container. What should be the volume in the container reported to the correct number of significant figures?

Carry out the following operations, and express the answer with the appropriate number of significant figures.863 x [1255 - (3.45 x 108)]

Consider the numbers 23.68 and 4.12. The sum of these numbers has ____ significant figures, and the product of these numbers has ____ significant figures.

A calculator is used to add and subtract measured masses: 43 g + 1.00 g - 2.008 g = 41.992 g What should the numeric answer be when expressed to the correct number of significant figures?

What is the meaning of the number of digits reported in a measured quantity?

What is the length of the pencil in the figure if the scale reads in centimeters?

What is the following number to four significant figures in standard exponential notation: 102.53070

How many milliliters of liquid does the smaller graduated cylinder contain? Express your answer in milliliters using the proper number of significant figures.

What is the correct reading for the liquid in this burette?(A) 32 mL(B) 32.2 mL(C) 32.26 mL(D) 33.74 mL

Which measurement is correct when using a 30-cm ruler with 0.1 cm markings? a) 10.1 cm b) -0.05 cm c) 5.225 cmd) 3.45 cm e) 29 cm

Read the water level with the correct number of significant figures.A) 87.20 mL B) 87.2 mL C) 87.2000 mL D) 87.200 mL E) 87 ml

Which measurement is expressed to 4 significant figures? 1) 0.00423 kg 2) 24.049 cm 3) 1300 K 4) 82,306 m5) 62.40 g

How many significant digits are in the following number? 150.0

A student weighs a flask (222g) and adds to this flask 4.325g of glucose (C6H12O6) and 35.5g of water. Properly expressed in significant figures, the total mass of this flask, sugar and water is now (in grams):a) 261.82b) 261.825c) 262d) 261.8 e) 261

Identify the exact numbers in this list. Select all that apply. (a) 56.00 s (a time measured by a stopwatch) (b) 4 choices (the number of choices in this list) (c) 2.54 cm (the number of centimeters in exactly 1 in) (d) 3 lbs (the weight of an object measured on a scale)

Which of these best expresses 0.0030950 in exponential notation to three significant figures?

How many significant figures are there in the number 0.0003677?

How many significant figures are there in the answer for the following problem?A) one B) two C) three D) four

The mass of a glass beaker is known to be 24.8 g. Approximately 5 mL of water are added, and the mass of the beaker and water is measured on an analytical balance to be 30.625 g. How many significant figures are there in the mass of the water?

The following statements are all true.a.
Jessica's house is 5 km from the grocery store.b.
Jessica's house is 4.73 km from the grocery store.c.
Jessica's house is 4.73297 km from the grocery store.What sort of device would Jessica need to make the measurement in each
statement?

Which of the following has 4 significant figures?A. 0.0042B. 1.054C. 1.30 x 102D. 1300E. 2.0004

Express 96,342 m using 2 significant figures. 1) 9.60 x 104 m 2) 9.6 x 10-4 m 3) 9.6 x 104 m 4) 96,000. m 5) 9.60 x 10-4 m

Read the length of the metal bar with the correct number of significant figures.A) 20 cmB) 15 cmC) 15.1 cmD) 15.10 cmE) 15.100 cm

Translate the following numbers into standard notation, maintaining the same number of significant figures. a. 4.52 x 103 b. 8.11 x 10-2

How many significant figures are in the number 0.80610?