SIGNIFICANT FIGURES Measured Data Counted Defined Data exact

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. .

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 0. 0027 g 6. 000 m 10. 002 g 0. 0050 g 50. 0500 g • • 2 SF 3 SF 2 SF 4 SF 5 SF 2 SF 6 SF

More Examples • • • 100 mm 10. 0 cm 1000 m. L 1000. 0 m. L • • • Indeterminate SF 3 SF Indeterminate SF 4 SF 5 SF

1000 m. L written so it has • • 1 SF 2 SF 3 SF 4 SF • • 1 x 103 m. L 1. 000 x 103 m. L

Counted Data • There were 15 cars in the parking lot. – Number is really 15. 00000. . • Number of significant figures is infinite • There were 20 students in the classroom – Number is really 20. 00000. . • Number of significant figures is infinite

Defined Data • There are 12 inches in a foot – Number is really 12. 00000. . • Number of significant figures is infinite • There are 100 centimeters in a meter – Number is really 100. 00000. . • Number of significant figures is infinite

More Examples • • 22. 7 g 100 people 100 m. L 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 • 11. 22 m (4. 23 m) = 47. 4606 m 2 • 11. 21 m ( 4. 22 m) = 47. 3062 m 2 • 11. 20 m (4. 21 m) = 47. 152 m 2

Rule for Multiplication / Division • The answer can only have as many significant figures as the number with the fewest significant figures. • 11. 21 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. • 1. 147 m + 15. 2 m = 16. 3 m • 3 DP + 1 DP = 1 DP

Mixed Arithmetic