Significant Figures



Significant Figures

1. Zeros that come before the first nonzero digit are not significant

2. Zeros that come after the last nonzero digit are significant if the number is a decimal, but if it is a whole number (no decimal point), they may or may not be significant. Get around this ambiguity by using scientific notation

3. Multiplying and Dividing: Final answer should have the same number of significant figures as there are in the number with the fewest significant figures. SIG FIGS ARE COUNTED

4. Adding and Subtracting: The number of sig figs in each number doesn’t matter. Answer is given to the same number of decimal places as the term with the fewest decimal places. DECIMAL PLACES ARE COUNTED

Rounding

1. If 1st digit removed is < 5, round down by dropping it and all other digits after it.

5.66 4525 becomes 5.66

2. If 1st digit removed is > 5, round up by adding 1 to the digit on the left.

5.6 64525 becomes 5.7

3. If 1st digit you remove is 5 and there are more nonzero digits following, round up. 6.664 525 becomes 6.665

4. If 1st digit you remove is 5 with nothing following, round down. 5.66452 5 becomes 5.66452 to 6 sig figs.

Combining calculations

Use correct order of operations, determining number of sig figs for each step and then determine number sig figs in final answer.

34.53 + (2.0342 x 16.2) = 34.53 + 32.954 ≈ 34.53 + 33.0 = 67.5 - 3 Sig Figs.

(34.53 + 2.0342) x 16.2 = 36.5642 x 16.2 ≈ 36.56 x 16.2 = 592 - 3 Sig Figs.

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