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SIGNIFICANT FIGURES
All non-zero figures are significant: 112.6 has four sig. figs.
All zeroes between non-zero figures are significant: 108.005 has six sig. figs.
Zeroes to the right of a non-zero figure, but to the left of an understood decimal point are NOT significant unless indicated to be significant (usually a line over the zero or listed in standard scientific notation) 200 has one sig. fig. and 2.00 x 102 has three sig. figs.
All zeroes to the right of a decimal point, but to the left of a non-zero figure, are NOT significant: 0.00647 has three sig. figs.
All zeroes to the right of a decimal point and following a non-zero figure are significant: both 0.07080 and 20.00 have four sig. figs.
Rules for Addition and Subtraction (think place!) The answer should have the same number of decimal places as the quantity have the least number of decimal places: 10.6 cm + 3.34 cm = 13.9 cm
Rules for Multiplication and Division (think number!) The number of significant figures should NOT be greater than the number of significant figures in the least precise factor: 6.2 cm x 3.44 cm = 21 cm2
Rules for Rounding:A. If the digit to be dropped is less than five, simple eliminate it.
134.3 g to 3 sig. Figs. = 134 g
B. If the digit to be dropped is more than five, (or a 5 followed by any non zero)
add 1 to the preceding digit.
134.6 g to 3 sig. Figs. = 135 g 134.501 g to 3 sig. figs. = 135 g
If the digit to be dropped is five, inspect the preceding digit.
If it is even, simply eliminate the five. 134.5 g to 3 sig. Figs. = 134 g
If it is odd, add 1 to the preceding digit. 133.5 g to 3 sig. Figs. = 134 g
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