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Scientific notation is used to turn small or large inconvenient numbers into manageable ones.

Concept #1: Understanding Scientific Notation

**Transcript**

Now, majority of you may remember scientific notation in algebra or from of course you recently take it. Now, scientific notation is a way of changing very large or very small numbers into more manageable ones, scientific notation is really a simple type of idea, but it's going to form the basis of all our chemical calculations from this point on. Now, in order to understand scientific notation you just have to remember the three components that make it up. So, let's take a look at this number, we have 6.88 times 10 to the negative 12, we're going to say the first number 6.88 is called the coefficient and the thing about the coefficient is, the coefficient must be greater than or equal to 1 but less than 10. So, that's the range that we're dealing with, we're going to say that the second number, which is the 10, is known as the base and when it comes to scientific notation the base is always 10, that's not ever going to change, finally we're going to say in 6.88 times 10 to the negative 12, the negative 12 number is known as our exponent. So, those are the three portions that make up any scientific notation number that you're given. So, just remember the guidelines for some of them and you'll be fine.

A scientific notation value is comprised of 3 parts: the **coefficient**, **base** and **exponent**.

Example #1: Convert the following numbers into scientific notation.

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Concept #1: Scientific Notation

Example #1: Convert the following numbers into scientific no...

Write the following number in scientific notation and round off to five significant figures: 0.00392708 x 10 81 .
a) 3.9271 x 10 84
b) 3.9270 x 10 78
c) 0.39271 x 10 78
d) 3.9270 x 10 80
e) 3.9271 x 10 78

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.

Use scientific notation to express each quantity with only the base units (no prefix multipliers). a. 4.5 ns

Use scientific notation to express each quantity with only the base units (no prefix multipliers). b. 18 fs

Use scientific notation to express each quantity with only the base units (no prefix multipliers). c. 128 pm

Use scientific notation to express each quantity with only the base units (no prefix multipliers).d. 35 µm

Convert the following measurements from scientific notation to standard notation: 6.4100 x 102 km

Convert the following into correct scientific notation: 851 x 10 −2

Express each of the following numbers in exponential notation with correct significant figures:(b) 0.03344

Which of the following are equal to 5 × 1010?Check all that apply.a. 50 × 109b. 50 × 1011c. 0.5 × 1011d. 500 × 108Scientific notation can be used to express very large or very small numbers more easily. For example,299800000 = 2.998 × 1080.00000509 = 5.09 × 10− 6In Mastering Chemistry, you may enter answers in scientific notation in the following format:2.998*1085.09*10-6

Which of the following are equal to 5 × 1010? Check all that apply. a) 0.5 × 1011 b) 50 × 1011 c) 50 × 109 d) 500 x 108

4.3×10-6 is between which two numbers?a) 1×10-7 and 1×10-8b) 1×10-6 and 1×10-7c) 1×10-5 and 1×10-6d) 1×10-4 and 1×10-5

The average thickness of a human hair is about 100 microns (m).Write it in scientific notation.

Convert the number 0.000127 to scientific notation, then enter the answer using a power of 10. You can select the button for scientific notation from the templates menu.Scientific notation can be used to express very large or very small numbers more easily. For example,299800000 = 2.998 × 1080.00000509 = 5.09 × 10− 6In Mastering Chemistry, you may enter answers in scientific notation in the following format:2.998*1085.09*10-6

Express the following number in scientific notation 0.000275 _____________________How many significant figures in your answer _______________

How do you write 0.005 in scientific notation?

Write the following number in scientific notation and round off to three significant figures: 31152 x 10-15 .

Express the circumference of the Earth at the Equator, 40,075,017 m, in scientific notation.

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

4.3 × 10−6 is between which two numbers?a. 1 × 10−7 and 1 × 10−8b. 1 × 10−6 and 1 × 10−7c. 1 × 10−5 and 1 × 10−6d. 1 × 10−4 and 1 × 10−5Scientific notation can be used to express very large or very small numbers more easily. For example,299800000 = 2.998 × 1080.00000509 = 5.09 × 10− 6In Mastering Chemistry, you may enter answers in scientific notation in the following format:2.998*1085.09*10-6

Express the following quantities in scientific notation using fundamental SI units of mass and length given in the table below.The Seven Fundamental SI Units of MeasurePhysical QuantityName of UnitAbbreviationMasskilogramkgLengthmetermTemperaturekelvinKAmount of substancemolemolTimesecondsElectric currentampereALuminous intensitycandelacdThe mass of carbon dioxide emitted from a large power plant each year, 20
Tg.

4.3×10-6 is between which two numbers?a) 1×10-7 and 1×10-8b) 1×10-6 and 1×10-7c) 1×10-5 and 1×10-6d) 1×10-4 and 1×10-5

Which of the following can be reduced to a single number in standard form?3√3 + 5√82√5 + 3√45√7 + √94√2 + 3√6

The average thickness of a human hair is about 100 microns (m).Write it in scientific notation.

Express each of the following numbers in scientific notation with correct significant figures:(a) 711.0

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