### Math With Significant Figures

Addition and Subtraction

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In mathematical operations involving significant figures, the answer is reported in such a way that it reflects the reliability of the least precise operation. Let's state that another way: a chain is no stronger than its weakest link. An answer is no more precise that the least precise number used to get the answer. Let's do it one more time: imagine a team race where you and your team must finish together. Who dictates the speed of the team? Of course, the slowest member of the team. Your answer cannot be MORE precise than the least precise measurement.

For addition and subtraction, look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do:

1) Count the number of significant figures in the decimal portion of each number in the problem. (The digits to the left of the decimal place are not used to determine the number of decimal places in the final answer.)

2) Add or subtract in the normal fashion.

3) Round the answer to the LEAST number of places in the decimal portion of any number in the problem.

WARNING: the rules for add/subtract are different from multiply/divide. A very common student error is to swap the two sets of rules. Another common error is to use just one rule for both types of operations.

**Practice Problems**

1) 3.461728 + 14.91 + 0.980001 + 5.2631

2) 23.1 + 4.77 + 125.39 + 3.581

3) 22.101 - 0.9307

4) 0.04216 - 0.0004134

5) 564,321 - 264,321

Remember to check the decimal portions of each number in the problem. For example, in the second problem, the 23.1 will dictate the significant figures in the decimal portion of the answer. In other words, NO MATTER how many significant figures there are in the whole number part (to the left of the decimal place), the answer to problem number 2 will extend only into the tenth place.

look at the answers.

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