Counting significant figures
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Counting Significant Figures. A Procedure for Counting Significant Digits How can you avoid counting zeros that serve merely to locate the decimal point as significant figures? Follow this simple procedure:

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Counting Significant Figures

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Counting significant figures

Counting Significant Figures

A Procedure for Counting Significant Digits

How can you avoid counting zeros that serve merely to locate the decimal point as significant figures? Follow this simple procedure:

1. Move the decimal point so that it is just to the right of the first nonzero digit, as you would in converting the number to scientific notation.

2. Any zeros the decimal point moves past are not significant, unless they are sandwiched between two significant digits.

3. All other figures are taken as significant.


Counting significant figures

Measurement Converted toScientific Significant

NotationFigures

0.01234 kg1.234 x 10-2 kg4Leading zeros (0.01234 kg) just locate the decimal point. They're never significant.

0.012340 kg1.2340 x 10-2 kg5Notice that you didn't have to move the decimal point past the trailing zero (0.012340 kg) so it doesn't vanish and so is considered significant.

0.000011010 m1.1010 x 10-5 m5Again, the leading zeros vanish but the trailing zero doesn't.

0.3100 m3.100 x 10-1 m4Ditto.

321,010,000 miles3.2101 x 106 miles5 (at least)Ignore commas. Here, the decimal point is moved past the trailing zeros (321,010,000 miles) in the conversion to scientific notation. They vanish and should not be counted as significant. The first zero (321,010,000 miles) is significant, though, because it's wedged between two significant digits.


Counting significant figures

Measurement Converted toScientific Significant

NotationFigures

84,000 mg8.4 x 104 mg2 (at least) The decimal point moves past the zeros (84,000 mg) in the conversion. They should not be counted as significant.

32.00 mL3.200 x 101mL4 The decimal point didn't move past those last two zeros. They are significant.

302.120 lbs3.02120 x 102 lbs 6 The decimal point didn't move past the last zero (302.120 lbs), so it is significant. The decimal point did move past the 0 between the two and the three, but it's wedged between two significant digits, so it's significant as well. All of the figures in this measurement are significant.


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