Question

1. write six conversion factors involving these units of measure: 1 g = 10² cg = 10³ mg.

Explanation:

Step1: Recall conversion - factor concept

A conversion factor is a ratio equal to 1 that is used to convert from one unit to another. Given \(1\ g = 10^{2}\ cg=10^{3}\ mg\).

Step2: First two conversion - factors

From \(1\ g = 10^{2}\ cg\), we can get \(\frac{1\ g}{10^{2}\ cg}=1\) and \(\frac{10^{2}\ cg}{1\ g}=1\).

Step3: Second two conversion - factors

From \(1\ g = 10^{3}\ mg\), we can get \(\frac{1\ g}{10^{3}\ mg}=1\) and \(\frac{10^{3}\ mg}{1\ g}=1\).

Step4: Third two conversion - factors

From \(10^{2}\ cg = 10^{3}\ mg\), we can get \(\frac{10^{2}\ cg}{10^{3}\ mg}=1\) and \(\frac{10^{3}\ mg}{10^{2}\ cg}=1\).

Answer:

\(\frac{1\ g}{10^{2}\ cg}\), \(\frac{10^{2}\ cg}{1\ g}\), \(\frac{1\ g}{10^{3}\ mg}\), \(\frac{10^{3}\ mg}{1\ g}\), \(\frac{10^{2}\ cg}{10^{3}\ mg}\), \(\frac{10^{3}\ mg}{10^{2}\ cg}\)