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Accuracy & Precision | 5 mins | 0 completed | Learn |
Standard Deviation, Mean, Median & Mode | 7 mins | 0 completed | Learn |
Metric Prefixes | 17 mins | 0 completed | Learn Summary |
Significant Figures | 18 mins | 0 completed | Learn Summary |
Energy, Heat and Temperature | 7 mins | 0 completed | Learn Summary |
Physical & Chemical Changes | 7 mins | 0 completed | Learn Summary |
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Significant Figures are used to determine some level of accuracy within our recorded measurements.
Concept #1: Determining significant figures
Transcript
We're going to say that we know that there is some level of accuracy and precision necessary with all of our calculations. But when we get an answer, how many digits does that answer have to have? That's when significant figures come into play and play a very important role in deciding the number of digits in our answer.
Now sig figs can be really easy as long as we remember two simple rules. It has to do with decimal places or no decimal places. Let's take a look at these two rules.
We're going to say rule one has to do with if you have a decimal point. We're going to say, if your number has a decimal point, we're going to move from left to right, so we're going to move from left to right. We're going to start counting once we get to our first non-zero number and keep counting until we get to the very end.
Now, rule number two is, if our number has no decimal point. If it has no decimal point, then you're going to start moving from right to left. We're going to start counting once we get to our first non-zero number and keep counting until you get to the very end.
Now, that we've seen these two simple rules, let's apply them to these examples.
Example #1: How many sig figs does each number contain?
0.0000185 m 749 mol
17.3 x 10^{3} mL 100. min
0.0010050 kg 1560 mol
Example #2: Read the length of the metal bar to the correct number of significant figures.
Concept #2: Understanding calculations with Significant Figures
Transcript
We’re going to say, when it comes to calculations we separate them into two categories. Multiplication and division go together; addition and subtraction will go together.
So we are going to say here when it comes to multiplication and division, measurements with the least number of significant figures, I’m just going to say sig figs, will determine our final answer. And when it comes to addition and subtraction we are going to say measurements with the least number of decimal places will determine our final answer.
So just remember when we are multiplication or division, we’re looking at the number of sig figs for our measurements. The one with the smallest number of sig figs will determine the number of sig figs in our final answer.
When we are doing addition and subtraction we want to get the fewest number of decimal positions that will give us our final answer.
The number of significant figures involved in a calculation depends on whether we are adding, subtracting, multiplying or dividing.
Example #3: Perform the following calculation to the right number of sig figs:
(3.16) x (0.003027) x (5.7 x 10^{-3})
Whenever we are adding or subtracting numbers with different exponents we must manipulate them to one common exponent value. We manipulate the values to get the least number of decimal places.
Example #4: Perform the following calculation to the right number of sig figs:
2.628 x 10^{6}
6.281 x 10^{4}
+ 0.827 x 10^{7}
Whenever we are dealing with a mixture of functions just remember your order of operations.
Example #5: Perform the following calculation to the right number of sig figs:
(42.00 – 40.915) • (25.739 – 25.729)
(11.50 • 1.001) + (0.00710 • 700.)
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