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

Determine the number of significant figures in each of the following measurements:
(a) $4867 \mathrm{mi}$, (b) $56 \mathrm{~mL}$, (c) 60,104 tons,
(d) $2900 \mathrm{~g}$,
(e) $40.2 \mathrm{~g} / \mathrm{cm}^{3}$, (f) $0.0000003 \mathrm{~cm},(\mathrm{~g}) 0.7 \mathrm{~min}$,
(h) 46 amu.

Key Concepts

Use of Scientific Notation

Scientific notation is often employed to clearly state the number of significant figures, especially in cases where trailing zeros might be ambiguous. By writing a number in scientific notation, only the explicitly stated digits are considered significant, which removes any doubt about the precision of the measurement.

Measurement Precision

Measurement precision is indicated by the number of significant figures, revealing how close repeated measurements are to one another. More significant figures imply a more precise measurement, which in turn affects how the measurement can be used in calculations and the trust one can place in its accuracy.

Significant Figures

Significant figures refer to the digits in a number that contribute to its measurement resolution. They indicate the precision of the measured or calculated value and help communicate the uncertainty inherent in the measurement process.

Rules for Identifying Significant Figures

The rules for determining significant figures include that all nonzero digits are considered significant; any zeros between nonzero digits (captive zeros) are significant; leading zeros, which precede all nonzero digits, are not significant; and trailing zeros in a number with a decimal point are significant, whereas trailing zeros without a decimal point can be ambiguous and require clarification.

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