Significant Figures GENERAL RULES Nonzero Integers are ...

[Pages:2]CHEM 100

Significant Figures GENERAL RULES

1. Nonzero Integers are always significant a. 532 ? 3 sig figs

2. Leading zeros are not significant a. 0.0025 ? 2 sig figs

3. Zeros between numbers are significant a. 54032 ? 5 sig figs

4. Trailing zeros are significant if the number has a decimal place a. 100. ? 3 sig figs b. 1.00 x 102 - 3 sig figs ? best approach is to write in scientific notation c. 100 ? 1 sig fig

5. Exact numbers have infinite significant figures a. 12 inches in 1 foot i. 12 is exact and we therefore don't worry about the number of sig figs

Think of Sig Figs in Terms of Measurements

Problem: How many sig figs in 10.3? How many sig figs in 0.0103?

Why are they the same?

Again, think in terms of measurements. Think of 10.3 as 10.3 g and 0.0103 as 0.0103 kg. The two numbers are the same expressed with different units so they should have the same number of significant figures.

Calculations and Sig Figs

1. Add - When adding and subtracting, the sig figs in your answer is limited by the decimal place.

0.75 +0.75 + 0.754 = 2.25

Find the Average (0.75 + 0.75 + 0.754) / 3 = 0.75

* Number of sig figs does not depend on 3 since 3 is an EXACT number and therefore has an infinite number of sig figs!

2. Multiply/Divide ? the sig figs in your answer are limited by the measurement with the least number of sig figs!

4.56 x 1.4 = 6.4 (NOT 6.38) since the lowest amount of sig figs is 2 for the # of sig figs in 1.4

3. When doing COMPLEX calculations, always round at the end!!!

"You can only be as precise as your instrument and as your least precise measurement"

Uncertainty in Measurements

Beaker 1. smallest division of a beaker is 10 mL so we can read to +/- 1 mL or 1/10 the smallest division

Graduated Cylinder 1. smallest division of a graduated cylinder is 1 mL so we can read to +/- 0.1 mL or 1/10 the smallest division a. if you have exactly 25 mL then you write 25.0 mL i. 25 mL means 25 +/- 1 mL (would be for a beaker) ii. 25.0 mL means 25 +/- 0.1 mL

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