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

Determine the number of significant figures in each of the following measurements: (a) 0.006 L, (b) 0.0605 dm, (c) 60.5 $\mathrm{mg},(\mathrm{d}) 605.5 \mathrm{cm}^{2},(\mathrm{e}) 9.60 \times 10^{3} \mathrm{g},(\mathrm{f}) 6 \mathrm{kg},(\mathrm{g}) 60 \mathrm{m}$

Key Concepts

Scientific Notation

Using scientific notation is an effective way to express numbers and clearly indicate the number of significant figures. In this format, all digits in the coefficient (mantissa) are considered significant, which eliminates ambiguity in counting significant figures.

Trailing Zeros

Trailing zeros are the zeros at the end of a number. Their significance depends on the presence of a decimal point; if a decimal point is present, these zeros are counted as significant because they indicate measured precision, while if no decimal point is present, their significance can be ambiguous without further context.

Significant Figures

This concept refers to the number of digits in a measured or computed quantity that are known with certainty, plus one final digit that is estimated. It reflects the precision of a measurement and is crucial for ensuring that the reported measurement matches the instrument’s accuracy.

Leading Zeros

Leading zeros are the zeros that precede all nonzero digits. They serve only as placeholders to indicate the scale or magnitude of the number and are not counted as significant figures in a measurement.

Captive Zeros

These are zeros that are located between nonzero digits within a number. They are always considered significant because they are part of the measured value and contribute to the precision of the number.

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