Round off the following quantities to the number of...

Round off the following quantities to the number of significant figures indicated in parentheses: $$ \begin{array}{ll}{\text { (a) } 7.0001 \mathrm{kg}(4)} & {\text { (b) } 1.605 \mathrm{km}(3)}\end{array} $$ $$ \begin{array}{ll}{\text { (c) } 13.2151 \mathrm{g} / \mathrm{cm}^{3}(3)} & {\text { (d) } 2,300,000.1(7)}\end{array} $$

Round off the following quantities to the number of significant figures indicated in parentheses:
$$
\begin{array}{ll}{\text { (a) } 7.0001 \mathrm{kg}(4)} & {\text { (b) } 1.605 \mathrm{km}(3)}\end{array}
$$
$$
\begin{array}{ll}{\text { (c) } 13.2151 \mathrm{g} / \mathrm{cm}^{3}(3)} & {\text { (d) } 2,300,000.1(7)}\end{array}
$$

Key Concepts

Significant Figures

Significant figures indicate the digits in a number that contribute to its precision. They are used to express the certainty of a measurement, specifying how many digits are reliable. Only non-zero digits and certain zeros (such as those between significant digits or trailing zeros in a decimal) are considered significant.

Rounding Rules

Rounding to a specified number of significant figures involves adjusting the number so that only the desired number of digits remain, starting from the first non-zero digit. The digit immediately after the last desired digit determines whether the last remaining digit is increased or stays the same, which ensures that the number accurately reflects the intended precision.

Measurement Accuracy and Precision

Measurements often come with uncertainties, and significant figures are used to report results with an appropriate level of accuracy. Rounding to the correct number of significant figures helps prevent the appearance of false precision, indicating the true reliability of the measurement.

Scientific Notation

Scientific notation is a convenient way to represent numbers, especially very large or very small ones, while clearly showing the number of significant figures. It expresses numbers as a product of a coefficient (which holds the significant figures) and a power of ten, making it easier to handle and communicate precision.

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