Make the following conversions (conversion factors are given...

Make the following conversions (conversion factors are given in Table 1.3 ): (a) $42.6 \mathrm{kg}$ to lb (b) $1.62 \mathrm{lb}$ to $\mathrm{g}$ (c) 34 in. to $\mathrm{cm}$ (d) $37.2 \mathrm{km}$ to mi (e) 2.73 gal to $\mathrm{L}$ (f) 62 g to oz $(\mathrm{g}) \quad 33.61 \mathrm{qt}$ to $\mathrm{L}$ (h) $43.7 \mathrm{L}$ to gal (i) $1.1 \mathrm{mi}$ to $\mathrm{km}$ (j) $34.9 \mathrm{mL}$ to $\mathrm{fl}$ oz

Make the following conversions (conversion factors are given in Table 1.3 ):
(a) $42.6 \mathrm{kg}$ to lb
(b) $1.62 \mathrm{lb}$ to $\mathrm{g}$
(c) 34 in. to $\mathrm{cm}$
(d) $37.2 \mathrm{km}$ to mi
(e) 2.73 gal to $\mathrm{L}$
(f) 62 g to oz
$(\mathrm{g}) \quad 33.61 \mathrm{qt}$ to $\mathrm{L}$
(h) $43.7 \mathrm{L}$ to gal
(i) $1.1 \mathrm{mi}$ to $\mathrm{km}$
(j) $34.9 \mathrm{mL}$ to $\mathrm{fl}$ oz

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Key Concepts

Dimensional Analysis

Dimensional analysis is a method used to check the consistency of equations and to facilitate the conversion between different units of measurement. By analyzing the dimensions (such as length, mass, and time) involved in a problem and using conversion factors, practitioners systematically ensure that expressions and equations adhere to the correct units, thereby preventing errors in calculations.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. This involves multiplying the given measurement by conversion factors, which are ratios that express the equivalence between different units for the same quantity. Understanding unit conversion is critical in mathematics, science, and engineering to ensure measurements are consistent and comparable across different systems.

Conversion Factors

Conversion factors are numerical ratios used to convert from one unit to another by expressing the relationship between two units. They serve as multipliers that cancel out the original unit and introduce the desired unit, ensuring that equations remain dimensionally consistent. Accurate conversion factors are essential for precise calculations in practical and theoretical contexts.

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