Practice on Significant Figures in Operations


Significant figures are a way of communicating the precision of a measurement; when the measurements are used to make calculations, this level of precision is carried through too. Scientists do this through the use of certain rules.

Using Significant Figures in Multiplication and Division

For multiplication and division, you must count the number of significant digits in each number to be multiplied or divided. Then, choose the smallest number of significant digits. This is the number of significant digits that should appear in your answer. For example, 12.32 cm x 4.2958 cm x 0.12 cm = 4 sig figs x 5 sig figs x 2 sig figs. So, your answer should have two significant figures.

Practice: What is 12.34 g / 6.29 mL?

  • 1.9
  • 1.96
  • 1.962
  • 1.961844
Practice: What is 0.00402 cm x 13.00 cm x 4306 cm?
  • 220
  • 230
  • 225
  • 225.0
Practice: What is 0.17362 x 31.22 x 170.06?
  • 922
  • 921.8
  • 921.80
  • 921.796
Practice: What is 9.042/(5.24 x 9.5)?
  • 0.2
  • 0.18
  • 0.181
  • 0.1816

Using Significant Figures in Addition and Subtraction

For addition and subtraction, evaluate each number to see what place the last significant digit is in. For example, the number 12.34 has the last significant digit in the hundreths place. Arrange the numbers in column form (as you did when you learned to add numbers by hand) and dircle the last significant digit. The last significant digit in the answer will be in the same place as the leftmost circle. This really isn't as hard as it sounds. Let's look at an example.

3.200 + 0.4968 + 24

(Last significant digit is in bold)3.200+0.4968+24

(Arrange in column form) 			
  3.200                                        			
  0.4968
+24
 ----------------
 27.6968
The answer would be 28; the last significant digit must be in the ones place.

Practice: 1.195 + 1320 + 41.263 =

  • 136
  • 1360
  • 1362
  • 1362.5
Practice: 9.026-9.019 =
  • 0.007
  • 0.0070
  • 0.00700
  • 0.007000
Practice: 150 + 1 + 0.182 =
  • 100
  • 150
  • 151
  • 151.2
Practice: 0.0428 + 1.00492 =
  • 1.04
  • 1.05
  • 1.047
  • 1.0477

Rounding rules

When performing operations such as above, it is often necessary to round numbers. After performing the operation and determining the correct number of significant figures, identify the digits that need to be rounded. There are three possibilities.

1. The digit(s) to be rounded off are less than 5 (or 0.5, or 0.05). The digits to be rounded then must begin with a 0, 1, 2, 3, or 4. Round these numbers down.

Practice: Round 442 to two significant figures.

  • 400
  • 440
  • 442
  • 450
Practice: Round 0.0539 to one significant figure.
  • 0
  • 0.0
  • 0.05
  • 0.06
2. The digit(s) to be rounded off are equal to or more than 500 (or 0.500, or 0.050). Round these numbers up.

Practice: Round 4501 to one significant figure.

  • 4000
  • 5000
Practice: Round 0.060185 to three significant figures.
  • 0.06
  • 0.0601
  • 0.0602
  • 0.06018
Practice: Round 0.006251 to four significant figures.
  • 0.006
  • 0.0062
  • 0.00625
  • 0.006251
Practice: Round 1.53499 to two significant figures.
  • 1.5
  • 1.53
  • 1.535

Using Significant Figures

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