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SIGNIFICANT FIGURES AMOLE 2015

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?

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

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 = ?

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 = ?

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 = ?

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 = ?

 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)

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.

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

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

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

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

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

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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