- SIGNIFICANT FIGURES:
When measuring things, scientists are always careful to express numerical values to the correct number of significant figures:
1 cm really means 1 cm + or - 0.5 cm, or between 0.5 and 1.5 cm
1.0 cm really means 1 cm + or - 0.05 cm, or between 0.95 and 1.05 cm
1.00 cm really means 1 cm + or - 0.005 cm, or between 0.995 and 1.005 cm
1.000 cm really means 1 cm + or - 0.0005 cm, or between 0.9995 and 1.0005 cm
1.000000 cm really means 1 cm + or - 0.0000005 cm, or between 0.9999995 and 1.0000005 cm
- PRECISION: The + or - amount in the expressions above is called the precision of the measurement.
Scientists (and science teachers) consider it a bad mistake to state the precisiopn incorrectly
by using the wrong number of significant figures.
When measuring, you should only state the number of significant figures that your measuring instrument allows.
For example, when measuring length with a ruler whose smallest marks are in tenths of a centimeter, your measurement
should only show tenths of a centimeter, not hundredths or thousandths: 1.8 cm, not 1.80 or 1.800 (or 2 cm).
- COUNTING SIGNIFICANT FIGURES:
Count the number of nonzero digits in your numerical expression.
Also include zeroes between nonzero digits or to the right of nonzero digits,
but NOT to the left of the nonzero digits. Thus:
- 1.2 cm has two significant figures
- 1.23 cm has three significant figures
- 1.203 cm has four significant figures because the zero counts
- 1.230 cm has four significant figures because the zero counts
- 01.23 cm has three significant figures (the zero does not count)
- 0.0123 cm has three significant figures (the zeroes do not count)
- 0.000000123 cm has three significant figures (the zeroes do not count)
When doing calculations, you should always round your results (up or down) to the correct number of significant figures.
Calculations involving several measurements should be rounded to the number of significant sigures in the
least precise measurement
(the one with the fewest significant figures). Thus,
when dividing 4.83527 grams by 1.2 milliliters, the answer should be
correctly written as 4.0 g/mL (two significant figures),
not 4.03 (three sig. figs.) or 4.02939 (six sig. figs.) because the 1.2 mL value has only two sig. figs.
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