Express the following with appropriate units and significant...

Express the following with appropriate units and significant figures: (a) $1.0 \mathrm{~m}$ plus $9 \mathrm{~mm}$, (b) $1.0 \mathrm{~m}$ times $1 \mathrm{~mm}$, (c) $1.0 \mathrm{~m}$ minus $998 \mathrm{~mm}$, and (d) $1.0 \mathrm{~m}$ divided by $998 \mathrm{~mm}$.

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Key Concepts

Units Conversion

Units conversion involves translating a measurement expressed in one unit into another unit while preserving its value. In many calculations, especially when combining terms with different units, it is essential to convert them into a common unit so that arithmetic operations make sense and the results are consistent.

Significant Figures

Significant figures are the digits in a measurement that carry meaningful information about its precision. When performing calculations, the result should be reported with the correct number of significant figures to reflect the precision of the input data, following the rules for addition, subtraction, multiplication, and division.

Arithmetic Operations with Units

Arithmetic operations with units, including addition, subtraction, multiplication, and division, require careful handling of both the numerical values and their associated units. In addition and subtraction, the operands must be in the same unit; for multiplication and division, the units combine according to algebraic rules, and the result must be expressed with proper units and appropriate precision based on significant figures.

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