Keeping Track of Significant Figures During Calculations

Rule 1: During Addition or Subtraction, round off to the first column (starting from the right column) that has an uncertain digit.

For numbers with digits to the right of the decimal point, this would mean rounding to the least number of decimal places.

Note: Remember that when you add or subtract two numbers, you must first line up the decimals before you add. For the same reason, if the numbers have exponents, the exponents must be adjusted to show the same number before you do the operation. The rule of determining the correct number of decimal places must be applied only after the exponents have been adjusted.

e.g. The answer to 0.03 + 0.02 x 10 ² is not 0.05 x10 ², nor 2.03 (even though both numbers have 2 decimal places.) The proper way to approach the problem:

0.03 + 0.02 x 10 ² = 0.03 + 2 = 2.03 = 2 (no decimal places).

Rule 4: When there are several steps before you get to the final answer, carry one extra digit and round off properly at the end. Often we keep track of the extra digit by writing a line through it.

Practice Exercise for Keeping Track of Significant Figures During Calculations:

1. 78.22 2. 7.26 3. 34 x 2 =

– 75.1 + 8.233

Do not take the exercise above simply as an arithmetic exercise! This is an exercise on significant figures! Work it out on paper before you check the answers provided below.

Ans to Practice Exercise above: 1) 3.1; 2) 15.49; 3) 7x10; 4) 4.00; 5) 0.80

If you did not obtain correct answers on ALL five questions, review the rules at the top of the page.

[Extra Practice: Brady & Senese 5^th Ed, p.21 Practice Exercises 5 & 6; p.31 #38 & 39]

[Extra Practice: Silberberg 4^th Ed, p.35 #58-67]