Carry out the following calculations, express the answers to...

Carry out the following calculations, express the answers to the correct numbers of significant figures, and include units in the answers. (a) $5280 \frac{\mathrm{m}}{\mathrm{km}} \times 6.2 \mathrm{~km}$ (b) $4.5 \mathrm{~m} \times 3.25 \mathrm{~m}$ (c) $2.50 \mathrm{~g} \div 8.3 \frac{\mathrm{g}}{\mathrm{cm}^{3}}$ (d) $4.70 \mathrm{~cm} \times 6.8 \mathrm{~cm} \times 2.54 \mathrm{~cm}$

Carry out the following calculations, express the answers to the correct numbers of significant figures, and include units in the answers.
(a) $5280 \frac{\mathrm{m}}{\mathrm{km}} \times 6.2 \mathrm{~km}$
(b) $4.5 \mathrm{~m} \times 3.25 \mathrm{~m}$
(c) $2.50 \mathrm{~g} \div 8.3 \frac{\mathrm{g}}{\mathrm{cm}^{3}}$
(d) $4.70 \mathrm{~cm} \times 6.8 \mathrm{~cm} \times 2.54 \mathrm{~cm}$

Key Concepts

Significant Figures

This concept involves maintaining the correct level of precision in numerical results based on the precision of the numbers used in the calculation. When performing arithmetic operations such as multiplication or division, the final answer should be rounded to the same number of significant figures as the number with the fewest significant digits among those used in the calculation.

Unit Conversion

Unit conversion is the process of converting a measured quantity from one unit to another using conversion factors. This is essential in ensuring that calculations are made using consistent units, and it often involves multiplying by a conversion factor that relates the two units.

Dimensional Analysis

Dimensional analysis is a technique used to verify that equations and calculations are consistent with respect to units. It involves tracking units throughout a calculation to ensure that the final result has the correct dimensional units, and it is particularly useful in checking conversion factors and the consistency of formulae.

Arithmetic Operations on Physical Measurements

This concept refers to the procedures for multiplying or dividing measured quantities while correctly handling both the numerical values and their associated units. It requires careful attention to the rules of significant figures and the proper management of units to ensure the final result is both numerically and dimensionally accurate.

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