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Physics

Physics. Significant Figures. Nonzero Digits. All nonzero digits are significant 1, 2, 3, 4, 5, 6, 7, 8, 9. Embedded Zeros. Embedded Zeros are Significant Zeros between other nonzero digits are significant 60.5 3,008 340,506. Leading Zeros. Leading Zeros are NOT significant

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Physics

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  1. Physics • Significant Figures

  2. Nonzero Digits • All nonzero digits are significant • 1, 2, 3, 4, 5, 6, 7, 8, 9

  3. Embedded Zeros • Embedded Zeros are Significant • Zeros between other nonzero digits are significant • 60.5 • 3,008 • 340,506

  4. Leading Zeros • Leading Zeros are NOT significant • Zeros in front of nonzero digits are not significant • 0.75 • .0032 • 0.0005

  5. Trailing Zeros • Trailing Zeros in a number with a decimal place ARE significant • Zeros that are at the end of a number containing a decimal place ARE significant • 5.0 • 33.20 • 4800.

  6. Trailing Zeros II • Trailing Zeros in a number without a decimal place are NOT significant • Zeros that are at the end of a number NOT containing a decimal place are NOT significant • 50 • 3320 • 4800

  7. How many Sig-Figs ? • a) 18.3 b) 183 c) .00183 d) 183.0 • e) 50 f) 505 g) .0050 h) 5000. • i) 200.00 j) 0.00220 k) 22020

  8. How many Sig-Figs ? • a) 18.3 3 b) 183 3 c) .00183 3 d) 183.0 4 • e) 50 1 f) 505 3 g) .0050 2 h) 5000. 4 • i) 200.00 5 j) 0.00220 3 k) 22020 4

  9. Addition & Subtraction • The final answer should have the same number of decimal places as the number with the least number of decimal places. • 90.3 + 2.23 = 92.53 = 92.5 • 180.1 + 5.202 + 3.32 = 188.632 = 188.6

  10. Multiplication & Division • The final answer has the same number of sig-figs as the number with the least number of sig-figs. • 123 x 5.35 = 658.05 = 658 • 16 x 2 = 32 = 30 • 16 x 2.0 = 32 = 32

  11. Express Result in Sig-Figs • 20.23 + 17.405 + .230 = ________ • 20.12 + 5.2 + .245 +100.4 = ________ • 5.35 x 20.2 x 5.0 = _______ • 2.00 x 500 = _______ • 2.5 x 55.5 = ________

  12. 20.23 + 17.405 + .230 = 37.865=37.86 • 20.12 + 5.2 + .245 +100.4 = 125.965=126.0 • 5.35 x 20.2 x 5.0 = 540.35 = 540 • 2.00 x 500 = 1000 • 2.5 x 55.5 = 138.75 = 140

  13. Round Down • Round Down whenever the digit following the last sig-fig is 0, 1, 2, 3 or 4 • Examples of #’s with 3 sig-figs: • 50.24 = 50.2 • 1.0038 = 1.00 • 230.29 = 230.

  14. Round Up • Round Up whenever the digit following the last sig-fig is a 6, 7, 8 or 9 • Examples of #’s with 3 sig-figs: • 183.6 = 184 • .053078 = .0531 • 23.46 = 23.5

  15. Rounding with 5’s I • Round UP if the digit following the last sig-fig is a 5 followed by a nonzero digit. • Examples with 3 sig-figs: • 23.451 = 23.5 • .018752 = .0188 • .102531 = .103

  16. Rounding with 5’s II • Round DOWN if the last sig-fig is an even # and the next digit is a 5, with no other nonzero digits. • Round UP if the last sig-fig is an odd # and the next digit is a 5, with no other nonzero digits. • Examples of #’s with 3 sig-figs: • 12.250 = 12.2 • 13.25 = 13.2 • 2.345 = 2.34 • 7.3850 = 7.38

  17. Express each in 3 Sig-Figs • a) 12.35 b) 100.5 c) .0001055 • d) 1.2251 e) 230,515 f) 456.5 • g) 223.50 h) 1000.5

  18. Answers • a) 12.35 b) 100.5 c) .0001055 • a) 12.4 b) 100. c) .000106 • d) 1.2251 e) 230,515 f) 456.5 • d) 1.23 e) 231,000 f) 456 • g) 223.50 h) 1000.5 • g) 224 h) 1000

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