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Sig Figs

Sig Figs. What are they?. In a measurement, some of the numbers we measure are an estimate. Significant Figures – The certain digits and first uncertain digits of a measurement. . We need to follow a set of rules to determine which numbers are significant. Rules.

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Sig Figs

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  1. Sig Figs

  2. What are they? In a measurement, some of the numbers we measure are an estimate. Significant Figures – The certain digits and first uncertain digits of a measurement. We need to follow a set of rules to determine which numbers are significant

  3. Rules 1. All non-zero numbers always count as significant figures. Ex. 175 has three sig figs. 2. Zero’s have three types: Leading zero’s – zeros that preceed all nonzero digits. Never count as sig fig. Ex. 0.0025 - 2 sig figs Captive zero’s – zeros between two nonzero digits. They are always significant Ex. 24.00029 - 7 sig figs Trailing zero’s – zero’s at the right end of a number. Only significant if there is a decimal point. 2 sig figs Ex. 1300 - 100 - 100. - 1 sig figs 3 sig figs

  4. Examples A. 7601 B. 0.032 C. 1.032 D. 43200 E. 600.00 F. 0.5006 G. 67.090 H. 1.23 x 1023 I 1.50 x 1023 • A. 4 • B. 2 • C. 4 • D. 3 • E. 5 • F. 4 • G. 5 • H. 3 • I . 3

  5. How to Use Sig Figs Your answer can only have the same number of Sig Figs as the lowest number in the calculation.

  6. Addition Add 12.11, 18.0, and 1.013 12.11 18.0 1.013 First step. Write them with their decimals lined up 1 decimal place Next: Add them up 31.123 The limiting term decides how many decimal places your answer can have. The limiting term is the number with the lowest decimal places Answer can only have the same number of decimal places 31.1

  7. Subtraction Same as Addition Ex. 1.06875 - 0.010 1.06875 - .010 Three decimal places 1.05875 1.059

  8. Practice 12.0089 + 2.34 +3.1440 = 8.6554 - 4.00870 = 10.7652 - 4.987 = 3.765 + 6.09840 + 10 = 17.49 4.6467 5.778 20

  9. Multiplication The answer can only contain the same number of sig figs as the lowest number used in the calculation. Ex 3.56 X 4.003 = 14.25068 3 sig figs 4 sig figs 14.3 So answer can only have 3 sig figs Division is the exact same

  10. Practice 5.0094 x 3.00 = 0.0054 x 27.992 = 2200 / 3.80 = 12.642642 / 5.0040 = 15.0 .15 580 2.5265

  11. Recap Addition/Subtraction The number with the lowest decimal places determines the number of decimal places in the answer Multiplication/Division The number with the lowest overall number of sig figs determines how many sig figs in the answer

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