What is the number of significant figures in each of the...

What is the number of significant figures in each of the following measurements?
(a) $4867 \mathrm{mi}$
(b) $56 \mathrm{~mL}$
(c) 60,104 ton
(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

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Key Concepts

Scientific Notation

Scientific notation is a method of expressing numbers as a product of a number (between 1 and 10) and a power of ten, which clearly shows the significant figures of the measurement. This format helps eliminate ambiguity, especially with very large or very small numbers, by ensuring that only the meaningful digits are presented.

Zeros in Measurements

The treatment of zeros in a measurement is essential for determining the correct number of significant figures. Leading zeros, which appear before the first non-zero digit, are not counted; captive zeros, which occur between non-zero digits, are always significant; and trailing zeros may or may not be significant based on whether a decimal point is present. This differentiation is fundamental in accurately conveying measurement precision.

Significant Figures

Significant figures are the digits in a number that contribute to its precision, indicating how accurately the number is measured or known. This concept includes all non-zero digits, any zeros between them, and in some cases, trailing zeros (particularly when a decimal point is involved), which all reflect the level of certainty in the recorded measurement.

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