Significant Figures
Why should I care if “100” has one significant figure or “100.0” has four?
Significant figures are very important in science. Each recorded measurement has a certain number of significant figures. Calculations done on these measurements must follow the rules for significant figures. The importance of a digit has to do with whether it represents a true measurement or not. Any digit that is actually measured or estimated will be considered significant. Placeholders, or figures that have not been measured or estimated, are not considered significant.
Rules for Significant Figures
1. Figures from 1-9 are always significant.
2. Zeros between two other significant figures are always significant
3. One or more additional zeros to the right of both the decimal place and another significant digit are significant.
4. Zeros used only for spacing the decimal point (placeholders) are not significant.
Recognizing significant figures will become much easier over time, as you continue to practice the rules. Below are some examples, which show the number of significant figures in a group of numbers, and an explanation why the figures are significant.
Table 1.1 Examples of Significant Figures
EXAMPLES / # OF SIG. FIG. / COMMENT453 kg / 3 / All non-zero figures are always significant.
5057 L / 4 / Zeros between 2 sig. fig. are significant.
5.00 / 3 / Additional zeros to the right of sig. fig and the decimal are significant.
0.007 / 1 / Placeholders are not sig.
Multiplying and Dividing
RULE: When multiplying or dividing, your answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.
Example: 22.37 cm x 3.10 cm x 85.75 cm = 5946.50525 cm3
We look to the original problem and check the number of significant digits in each of the original measurements:
22.37 shows 4 significant digits.
3.10 shows 3 significant digits.
85.75 shows 4 significant digits.
Our answer can only show 3 significant digits because that is the least number of significant digits in the original problem.
5946.50525 shows 9 significant digits, we must round to the tens place in order to show only 3 significant digits. Our final answer becomes 5950 cm3.
Adding and Subtracting
RULE: When adding or subtracting your answer can only show as many decimal places as the measurement having the least number of decimal places.
Example: When we add 3.76 g + 14.83 g + 2.1 g = 20.69 g
We look to the original problem to see the number of decimal places shown in each of the original measurements. 2.1 shows the least number of decimal places (2). We must round our answer, 20.69, to one decimal place (the tenth place). Our final answer is 20.7 g
Practice
Complete the following on a separate sheet of paper.
Determine the number of significant digits in each of the following:
a) 5.40 f) 1.2 x 103
b) 210 g) 0.00120
c) 801.5 h) 0.0102
d) 1,000 i) 9.010 x 10-6
e) 101.0100 j) 2,370.0
Add:
a) 16.5 + 8 + 4.37
b) 13.25 + 10.00 + 9.6
c) 2.36 + 3.38 0.355 + 1.06
d) 0.0853 + 0.0547 + 0.0370 + 0.00387
e) 25.37 + 6.850 + 15.07 + 8.056
Subtract:
a) 23.27 - 12.058 c) 350.0 - 200
b) 13.57 - 6.3 d) 27.68 - 14.369
Multiply:
a) 2.6 x 3.78 e) 3.08 x 5.2
b) 6.54 x 0.37 f) 0.0036 x 0.02
c) 3.15 x 2.5 x 4.00 g) 4.35 x 2.74 x 3.008
d) 0.085 x 0.050 x 0.655 h) 35.7 x 0.78 x 2.3
Divide:
a) 35 / 0.62 c) 0.58 / 2.1 e) 3.76 / 1.62
b) 39 / 24.2 d) 40.8 / 5.05 f) 0.075 / 0.030