Question

which of the following is a valid conversion factor? (\frac{1,000 \text{ml}}{1 \text{l}}) (\frac{1 \text{hm}}{1,000 \text{m}}) (\frac{1 \text{cm}^3}{1 \text{l}}) (\frac{1,000 \text{cg}}{1 \text{g}})

Explanation:

Step1: Recall unit conversions

• Volume: \(1\,\text{L} = 1000\,\text{mL}\), \(1\,\text{L} = 1000\,\text{cm}^3\) (since \(1\,\text{cm}^3 = 1\,\text{mL}\)).
• Length: \(1\,\text{hm} = 100\,\text{m}\) (hectometer to meter: "hecto" means 100).
• Mass: \(1\,\text{g} = 100\,\text{cg}\) (centigram to gram: "centi" means 1/100, so \(1\,\text{g} = 100\,\text{cg}\)).

Step2: Analyze each option

• Option 1: \(\frac{1000\,\text{mL}}{1\,\text{L}}\) – Since \(1\,\text{L} = 1000\,\text{mL}\), this is a valid conversion factor (equivalent to 1, so multiplying by it doesn't change the value, just the units).
• Option 2: \(\frac{1\,\text{hm}}{1000\,\text{m}}\) – But \(1\,\text{hm} = 100\,\text{m}\), so this is incorrect (should be \(\frac{1\,\text{hm}}{100\,\text{m}}\) or \(\frac{100\,\text{m}}{1\,\text{hm}}\)).
• Option 3: \(\frac{1\,\text{cm}^3}{1\,\text{L}}\) – Since \(1\,\text{L} = 1000\,\text{cm}^3\), the correct conversion factor would be \(\frac{1\,\text{cm}^3}{1\,\text{mL}}\) or \(\frac{1000\,\text{cm}^3}{1\,\text{L}}\), so this is incorrect.
• Option 4: \(\frac{1000\,\text{cg}}{1\,\text{g}}\) – Since \(1\,\text{g} = 100\,\text{cg}\), the correct conversion factor is \(\frac{100\,\text{cg}}{1\,\text{g}}\) or \(\frac{1\,\text{g}}{100\,\text{cg}}\), so this is incorrect.

Answer:

\(\boldsymbol{\frac{1000\,\text{mL}}{1\,\text{L}}}\) (the first option)