#576. Significant Figures Handout

Science, level: Senior
Posted Wed Aug 19 16:12:48 PDT 1998 by Michael H. Edmondson (medmond@hotmail.com).
Hardaway High School, Columbus, GA USA
Materials Required: Paper, pencil, calculator
Activity Time: One or two periods
Concepts Taught: Use of significant figures in science

SIGNIFICANT FIGURES

A "significant figure" is one which is known to be fairly reliable.

1. All digits that are not zero are significant.

Example: 16.2 (3 significant figures)
Example: 18,648 (5 significant figures)

2. Zeros between non zero digits are significant.

Example: 103 (3 significant figures)
Example: 100.01 (5 significant figures)

3. Zeros to the left of the first non zero digit are not significant. They indicate placement of the decimal point only.

Example: 0.02 (1 significant figure)

Example: 0.00009 (1 significant figure)

4. Zeros to the right of a decimal point are significant if they are at the end of a number.

Example: 16.0 (3 significant figures)
Example: 16.0000 (6 significant figures)

5. When a number ends in a zero or zeros that are not to the right of a decimal point, the ending zero or zeros may or may not be significant. To indicate significance, place the non zero digits and all zeros into scientific notation:

Example: 160. (3 significant figures, because decimal is expressed. 1.60 x 102
Example: 160 (2 significant figures - 1 and 6 - because no decimal is expressed, therefore the zero is not treated as being significant.) 1.6 x 102

SIGNIFICANT FIGURES: ADDITION AND SUBTRACTION

When adding and subtracting numbers with consideration for significant figures, line up decimals and add or subtract as normal. Then, look at the numbers which you added or subtracted. Whatever the least number of digits that are present in those added or subtracted numbers, to the right of the decimal, that must be the same number of digits to the right of the decimal in your final answer. You round off to get those digits. Notice that the only consideration is to be those digits which are to the right of the decimal in the added or subtracted numbers.

Example: 19.3 + 6.09 + .2 + 207.0 + 10

19.3
6.09
.2
207.0
+ 10
____________
242.59 = 243

Note that in the above example, in the final number being added (10) there are no digits to the right of the decimal. (In fact, there is no decimal.) Therefore, your final answer should have no digits to the right of the "decimal position."

Example: 1.987 + 10.6 + 10.23 + 10.921

1.987
10.6
10.23
+ 10.921
_________
33.738 = 33.7

Note that in this example, the least number of digits in the added numbers is one digit (in the 10.6.) Therefore, the final answer should have only one digit to the right of the decimal position.

SIGNIFICANT FIGURES: MULTIPLICATION AND DIVISION

When multiplying and dividing numbers with respect to significant figures, you look at the total number of digits that are present in each figure being multiplied or divided. Then, you note the number with the least total digits. When you obtain your final answer, round so that you have an answer with equal digits as the lowest number of digits present in any given number.

Example: 20.1 x 10.111 = 203.2311 = 203

Note that you round the final answer off so that you have 3 digits in it. 20.1 had three digits and you have in the final answer, digits equal to the least number of digits in any given number being multiplied or divided.

Example: 100 x 1000.23 = 100023

In this case, according to the significant figure rules for zeros, in the 100 there is only 1 significant figure. Therefore, your final answer must have only one digit in it:

Rounding 100023 = 1, but there is no sensible way that 100023 equals 1. What, then, do you do? You place the answer in scientific notation, so that the correct place value is held and you can at the same time hold the correct number of significant figures.

100023 = 1 x 105

Now you have held the answer to the hundred thousands (as you should) and shown the correct number of significant figures (which you so desired to do.)