Significant Figures

When you write down a measurement, the way you write the number tells which digits are certain and which digits are uncertain. The last digit is always uncertain. The certain digits plus the one uncertain digit are known as “significant figures.” For example, the number 2453 has four significant figures. The 2, 4 and 5 are certain, and the 3 is uncertain.

If a calculation has too many uncertain digits, you must round off your answer so that only one digit is uncertain.

There are rules for deciding which figures are significant.

The digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 are always significant.

Zeros are not significant when they appear at the end of a whole number without a decimal point. For example, 290 has only two significant figures.

Zeros are not significant when they appear at the beginning of a decimal without a whole number. For example, 0.003 has one significant figure, but 1.003 has four.

When adding or subtracting two numbers, your answer should have the same number of decimal places as the smallest number of decimal places in the numbers you’re using. For example, 1.445 + 7.6 = 9.0.

When multiplying or dividing two numbers, your answer should have the same number of significant figures as the smallest number of significant figures in the numbers you’re using. For example, 3.21(1.4489) = 4.65.

Problems

How many significant figures in each of the following?

1)   3.65                                                                   6)   6503

2)   22                                                                      7)   120.4

3)   14.50                                                 8)   8600

4)   4.0000                                                               9)   0.052

5)   650                                                                    10)   0.00680

Do the arithmetic, and give your answers using significant figures.

11)   3 ÷ 7.00 =                                                       15)   45 + 77.2 =

12)   752 ´ 13 =                                                      16)   2100 – 45.77 =

13)   34 ÷ 655 =                                                      17)   25.442 + 56.17 =

14)   2.008 ´ 720 =                                                 18)   180.00 – 18.668 =