SIGNIFICANT FIGURES Measured Data Counted & Defined Data (exact numbers) Calculated Data –Multiplication & Division –Addition & Subtraction

Significant Figures All the certain digits plus one uncertain digit.

X.XXX....

We Need Some Rules!!!

The 5 Rules All non-zero digits are significant. Zeros at the beginning of a number are not significant. Zeros to the right of a decimal point are significant IF they are preceded – anywhere in the number – by significant digits. Zeros between significant digits are significant. If a number ends in zeros and a decimal point is not shown, the number of significant figures is indeterminate.

Some Examples 1.2 m 1.25 m g m g g g 2 SF 3 SF 2 SF 4 SF 5 SF 2 SF 6 SF

More Examples 100 mm 10.0 cm 1000 mL mL mL Indeterminate SF 3 SF Indeterminate SF 4 SF 5 SF

1000 mL written so it has 1 SF 2 SF 3 SF 4 SF 1 x 10 3 mL 1.0 x 10 3 mL 1.00 x 10 3 mL x 10 3 mL

Counted Data There were 15 cars in the parking lot. –Number is really Number of significant figures is infinite There were 20 students in the classroom –Number is really Number of significant figures is infinite

Defined Data There are 12 inches in a foot –Number is really Number of significant figures is infinite There are 100 centimeters in a meter –Number is really Number of significant figures is infinite

More Examples 22.7 g 100 people 100 mL 100 cm in a m 10.0 s 10. mm 15 pennies 3 feet in a yard 3 SF Infinite SF Indeterminate SF Infinite SF 3 SF 2 SF Infinite SF

Sig Figs in Calculations Multiplication & Division

Uncertainty in Calculated Area m (4.23 m) = m m ( 4.22 m) = m m (4.21 m) = m 2

Rule for Multiplication / Division The answer can only have as many significant figures as the number with the fewest significant figures m (4.22 m) = 47.3 m 2 4 SF ( 3 SF ) = 3 SF

Sig Figs in Calculations Addition & Subtraction

Uncertainty in Total Length

Rule for Addition / Subtraction The answer can only have as many decimal places as the number with the fewest decimal places m m = 16.3 m 3 DP + 1 DP = 1 DP

Mixed Arithmetic