Significant Figures

Significant Digits or Significant Figures

• We must be aware of the accuracy limits of each piece of lab equipment that we use and record our data to the proper number of significant figures.

• You are always allowed one estimated figure in measurements

• When measured quantities are given to you, it is assumed that the proper number of significant figures were recorded.

Rules for Counting Significant Figures

• All non-zero digits are significant.1 473 _____ 785 _____ 387.56 ____

• Zeros:– Leading Zeros are not significant.

0.421 _____ 0.5 _____ 0.0011 _____– Captive Zeros are significant.

70 304 _____ 395.01 _____ 1.008 _____– Trailing Zeros are significant if there is a decimal point.

12.380 _____ 1.30 _____ 1691.100 _____– Trailing Zeros are not significant if there is no decimal point.

2 500 _____ 800 _____ 9 010 _____

7

3 5

3 1 2

5 5 4

5 3

4

2 1 3

Determine the amount of significant figures in the following examples:

967 _____0.111 0 _____0.005 670 _____4.530 _____2.700 _____0.006 007 _____9.67 _____0.000 008 _____0.800 008 _____

34

444

43

16

Calculating with Significant Figures

• Multiply/Divide: The number with the fewest number of sig figs will determine the number of sig figs in the answer.– Example

(13.92 g/cm3)(23.3 cm3 ) = 324.103 g4 sig figs 3 sig figs 3 sig figs

324 g

Calculating with Significant Figures

• Addition/Subtraction: The number with the fewest amount of decimal places determines the amount of decimal places in the answer .– Example

3.76 g + 14.83 g + 2.1 g = 20.69 g2 decimal

places

20.7 g

2 decimal places

1 decimal places

1 decimal places