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SIGNIFICANT FIGURES AMOLE 2015

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WHAT & WHY? Refer to them as “Sig Figs” for short Used to communicate the degree of precision measured Example - Scientists records: 50 mL Does that mean… 50 mL exact? Could he only measure to the ones place? Did he round up from 49.8? Is it really 50.12 mL?

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RULE #1: NON ZEROS Every nonzero digit is significant. If it’s not a zero, it will count Examples: 24 = 2 sig figs 3.56 = 3 sig figs 7 = 1 sig figs

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RULE #2: CAPTURED ZEROS Also called “trapped” or “sandwiched” zeros Zeros between non-zeros are significant Examples: 7003 = 4 sig figs 40.9 = 3 sig figs 60.09 = ?

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RULE #3: LEADING ZEROS Zeros appearing in front of non-zero digits are not significant Act as placeholders Can’t be dropped, show magnitude Examples: 0.00024 = 2 sig figs 0.453 = 3 sig figs 0.003 = ?

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RULE #4: TRAILING ZEROS Zeros at the end of a number with a decimal point are significant. At the end and to the right of a decimal point Examples: 43.00 = 4 sig figs 1.010 = 4 sig figs 1.50 = ?

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RULE #5: TRAILING ZEROS Zeros at the end of a number without a decimal point are not significant. At the end and to the right of a decimal point Examples: 300 = 1 sig figs 27,300 = 3 sig figs 120 = ?

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All non-zero digits DO count. Leading zeros DON’T count. (zeros in front of numbers) Captive Zeros DO count. (zeros between non-zero numbers) Trailing Zeros DO count IF the number contains a DECIMAL. (zeros at the end of numbers)

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TRY THESE! 4.012 87,900 91.0005 500,001 0.005 0.6010 7,040, 100 2.100 = 4 sig. figs. = 3 sig. figs. = 6 sig. figs. = 1 sig. figs. = 4 sig. figs. = 5 sig. figs. = 4 sig. figs.

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ADDING & SUBTRACTING The answer cannot be more precise than the values in the calculation The answer is rounded off so it contains the same decimal places as the number in the problem with the fewest. Example: 12.11 + 18.0 = 30.11 12.11 = 2 decimal places 18.0 = 1 decimal place 12.11 + 18.0 = 30.1

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YOU TRY: 2.140 + 0.023 = ? 2.140 = 3 decimal places 0.023 = 3 decimal places Answer unrounded: 2.163 Answer with appropriate sig figs: 2.163

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MULTIPLYING & DIVIDING The answer cannot be more precise than the values in the calculation Answer should contain the same number of sig figs as the number with the least sig figs in the problem: Example: 4.56 x 1.4 = 6.38 4.56 = 3 1.4 = 2 4.56 x 1.4 = 6.4

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YOU TRY: 1.20 x 0.51 = ? 1.20 = 3 0.51 = 2 Answer unrounded: 0.612 Answer with appropriate sig figs: 0.61

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TRY THESE! 4.01 + 0.03 87.957 – 85.1 4.13 x 1.2 500 / 5.5= 4.04 = 2.857= 2.9 = 4.956= 5.0 = 90.90909= 90

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PUTTING IT ALL TOGETHER (1.2 x 10 3 ) x (3 x 10 4 ) = ? (3.6 x 10 7 ) / (4.0 x 10 5 ) = ? (1.2 x 10 -3 ) x (3 x 10 4 ) = ? (3.6 x 10 7 ) / (4.0 x 10 -5 ) = ?

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