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SIGNIFICANT FIGURES

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.

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SIGNIFICANT FIGURES

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

  2. Significant Figures • All the certain digits plus one uncertain digit.

  3. X.XXX . . . .

  4. X.XXX . . . .

  5. We Need Some Rules!!!

  6. 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.

  7. 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 Some Examples

  8. 100 mm 10.0 cm 1000 mL 1000. mL 1000.0 mL Indeterminate SF 3 SF Indeterminate SF 4 SF 5 SF More Examples

  9. 1 SF 2 SF 3 SF 4 SF 1 x 103 mL 1.0 x 103 mL 1.00 x 103 mL 1.000 x 103mL 1000 mL written so it has

  10. 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

  11. 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

  12. 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 Infinite SF More Examples

  13. Sig Figs in Calculations Multiplication & Division

  14. Uncertainty in Calculated Area • 11.22 m (4.23 m) = 47.4606 m2 • 11.21 m ( 4.22 m) = 47.3062 m2 • 11.20 m (4.21 m) = 47.152 m2

  15. 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 m2 • 4 SF ( 3 SF ) = 3 SF

  16. Sig Figs in Calculations Addition & Subtraction

  17. Uncertainty in Total Length

  18. 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

  19. Mixed Arithmetic

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