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Significant Figures Chem 140

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Why significant figures? Weight of penny: 3 g ± 1 g Not very accurate Weight of truck: 41 057 214 g Also ± 1 g Much more accurate Cardinal Scale Mfg. Co.

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Why significant figures? Measure of accuracy 3 g Error: 33 % One significant figure

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Why significant figures? Measure of accuracy 3 g Error: 33 % One significant figure 41 057 214 g Error: 0.0000024 % Eight significant figures

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Rules for significant figures 1)Nonzero numbers: Always significant 2)Captive zeroes: Always significant 3)Leading zeroes: Never significant 4)Trailing zeroes: Significant when the decimal point is written

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Examples 13060

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Examples 13060 four s.f.

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Examples 13060 four s.f. 13060.

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Examples 13060 four s.f. 13060. five s.f.

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Examples 13060 four s.f. 13060. five s.f. 0.001040

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Examples 13060 four s.f. 13060. five s.f. 0.001040 four s.f.

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Examples 13060 four s.f. 13060. five s.f. 0.001040 four s.f. 6.022 × 10 23

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Examples 13060 four s.f. 13060. five s.f. 0.001040 four s.f. 6.022 × 10 23 four s.f.

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Multiplying and dividing The number with the fewest s.f. determines how many are in the result.

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Multiplying and dividing The number with the fewest s.f. determines how many are in the result. 0.043 × (6.022 × 10 23 ) = 2.58946 × 10 22

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Multiplying and dividing The number with the fewest s.f. determines how many are in the result. 0.043 × (6.022 × 10 23 ) = 2.58946 × 10 22 = 2.6 × 10 22

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Adding and subtracting Don’t count significant figures, count decimal places.

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Adding and subtracting Don’t count significant figures, count decimal places. 3.54 + 0.0152 = 3.5552

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Adding and subtracting Don’t count significant figures, count decimal places. 3.54 + 0.0152 = 3.5552

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Adding and subtracting Don’t count significant figures, count decimal places. 3.54 + 0.0152 = 3.5552 3.56

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Exact numbers Some numbers have infinite s.f. 60 seconds in a minute 2.54 cm in an inch 2 measurements being averaged

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