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Significant Figures

Significant Figures. What is a significant figure?. There are 2 kinds of numbers: Exact : Known with certainty. Example: the number of students in this room Approximate: anything MEASURED. Example: Mass, volume, length, weight, height No measurement is perfect.

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Significant Figures

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  1. Significant Figures

  2. What is a significant figure? There are 2 kinds of numbers: • Exact: Known with certainty. Example: the number of students in this room • Approximate: anything MEASURED. Example: Mass, volume, length, weight, height No measurement is perfect.

  3. When to use Significant figures • When a measurement is recorded only those digits that are dependable are written down.

  4. When to use Significant figures • If you measured the width of a paper with your ruler you might record 21.7cm. • To a mathematician 21.70, or 21.700 is the same.

  5. But, to a scientist 21.7cm and 21.70cm is NOT the same • 21.700 cm to a scientist means the measurement is accurate to within 1/1000 of a cm.

  6. But, to a scientist 21.7cm and 21.70cm is NOT the same • If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.

  7. How do I know how many Sig Figs? • Rule 1: All non zero digits are significant. Example: 1,246 (4 sig figs)

  8. How do I know how many Sig Figs? • Rule 2: Any zeros between significant digits are also significant. Example: 1,206 (4 sig figs)

  9. How do I know how many Sig Figs? • Rule 3: If the number does not contain a decimal point, any zeros to the right of a nonzero number are NOT significant Example: 1,200 (2 sig figs)

  10. How do I know how many Sig Figs? • Rule 4: If zeros are at the end of a number that has a decimal, the zeros are significant. Example: 1,200. (4 sig figs)

  11. How do I know how many Sig Figs? • Rule 5: If a value has no significant digits to the left of a decimal point, any zeros to the right of the decimal point before the non zero numbers (leading zeros) are not significant. Example: 0.0012 (2 sig figs)

  12. How do I know how many Sig Figs? • Rule 6: Zeros that are found after non zero numbers to the right of a decimal point are significant (trailing zeros) Example: 0.1200 (4 sig figs)

  13. How many sig figs? • 7 • 40 • 0.5 • 0.00003 • 7 x 105 • 7,000,000 1 1 1 1 1 1

  14. How many sig figs here? • 1.2 • 2100 • 56.76 • 4.00 • 0.0792 • 7,083,000,000 2 2 4 3 3 4

  15. How many sig figs here? • 3401 • 2100 • 2100.0 • 5.00 • 0.00412 • 8,000,050,000 4 2 5 3 3 6

  16. What about calculations with sig figs? • Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

  17. Add/Subtract examples • 2.45cm + 1.2cm = 3.65cm • round to = 3.7cm • 7.432cm + 2cm = 9.432 round to  9cm

  18. Multiplication and Division • Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

  19. A couple of examples • 56.78 cm x 2.45cm = 139.111 cm2 • round to  139cm2 • 75.8cm x 9.60cm = ? 728 cm2

  20. Have Fun Measuring and Happy Calculating!

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