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Our Friends, the Significant Figures

Our Friends, the Significant Figures. Significant Figures (“ Sig Figs ”). All digits in a measurement that are known for certain, plus the first estimated (uncertain) digit Sig figs give an indication of the degree of precision for a measurement and/or a calculation

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Our Friends, the Significant Figures

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  1. Our Friends, the Significant Figures

  2. Significant Figures (“Sig Figs”) • All digits in a measurement that are known for certain, plus the first estimated (uncertain) digit • Sig figs give an indication of the degree of precision for a measurement and/or a calculation • ONLY used when a number is (or is assumed to be) a measurement • EXACT quantities do not have “sig figs”

  3. Sig Fig Rules—Know and USE These! • Rules for determining how many sig figs are in a measurement: • All non-zero values ARE significant • i.e. 54 mm has 2 s.f.; 5400 m has 2 s.f. • All zeros between non-zero digits ARE significant • i.e. 504 N has 3 s.f. • For numbers LESS THAN 1: • Zeros directly after the decimal point are NOT significant • i.e. 0.00565 J has 3 s.f.

  4. Sig Fig Rules—Know and USE These! • A zero to the right of a decimal AND following a non-zero digit IS significant • 0.150 m has 3 s.f.; 15.0 kg has 3 s.f.; • All other zeros are NOT significant • Examples: How many sig figs in each of the following? • 15.035 cm • 0.0560 s • 35000 kg

  5. Scientific Notation and Sig Figs • Use Scientific notation when you need to specify how many zeros are significant • i.e. Write 1500 N with 3 s.f. • The best way to do this is with scientific notation: 1.50 x 103 N • Write 10600 kg with 4 s.f.

  6. Note on Book Problems • Most of the problems in your book will have values which look like they only have 1 s.f. • Assume that all digits in book problems are significant • i.e. if a problem says that an object has a mass of 100 kg, please treat that as 3 s.f. • We’ll be a lot pickier in your labs!

  7. Sig Figs in Calculations • When adding or subtracting: • Your answer must have the same degree of precision as the least precise measurement • (that means…go to the fewest number of decimal places) • i.e.: 24.2 g + 0.51 g + 7.134 g = 31.844 g  31.8 g

  8. Sig Figs in Calculations • When multiplying and dividing: • The number of sig figs in the answer is equal to the least number of sig figs in any of the measurements used in the calculation • i.e. 3.22 cm * 12.34 cm * 1.8 cm = 71.52264 cm3 72 cm3

  9. How many significant figures are in the following measurement: 415.2 cm

  10. How many significant figures are in the following measurement: 0.00065 s

  11. How many significant figures are in the following measurement: 1500 g

  12. How many significant figures are in the following measurement: 0.007250 W

  13. How many significant figures are in the following measurement: 105.00 cm

  14. What is the answer to the following calculation: 1.25 cm + 6.5 cm + 11.75 cm + 0.055 cm • 19.555 cm • 19.56 cm • 19.5 cm • 19.6 cm • 20.0 cm • 20 cm

  15. What is the answer to the following calculation: 25.50 m * 12.057 m * 0.095 m • 29.2080825 m3 • 29.2081 m3 • 29.208 m3 • 29.21 m3 • 29.2 m3 • 29 m3

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