Determine the number of significant figures in each of the...

Determine the number of significant figures in each of the following measurements: (a) 4867 mi, (b) 56 mL, (c) 60,104 tons,
(d) $2900 \mathrm{g},$ (e) $40.2 \mathrm{g} / \mathrm{cm}^{3},$ (f) $0.0000003 \mathrm{cm},$ (g) $0.7 \mathrm{min}$
(h) $4.6 \times 10^{19}$ atoms.

Key Concepts

Scientific Notation

Scientific notation is a method of writing very large or very small numbers in the form of a coefficient multiplied by a power of ten. An advantage of this notation is that it clearly conveys the number of significant figures by showing only the significant digits in the coefficient. This clarity removes any ambiguity about which zeros are significant, simplifying the process of determining the precision of a measurement.

Significant Figures

Significant figures are the digits in a numerical measurement that contribute to its precision. They represent all known digits plus one estimated digit, reflecting the certainty in the measurement. Correctly identifying significant figures is crucial to ensure that the precision of the measurement is appropriately communicated and that calculations do not imply a false level of accuracy.

Rules for Counting Significant Figures

There are several standard rules for determining the number of significant figures in a number. First, all nonzero digits are significant. Second, any zeros between nonzero digits are also significant. Third, leading zeros (zeros to the left of the first nonzero digit) are not significant, as they only serve to position the decimal point. Finally, trailing zeros in a number that contains a decimal point are considered significant; however, in whole numbers without a written decimal point, trailing zeros can be ambiguous unless additional notation (like a bar over the zero or scientific notation) is used to indicate significance.

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