Question

1×10^{6} g solution × \frac{1}{1.01} \frac{ml}{g} × \frac{10^{-3}}{1} \frac{l}{ml}

Explanation:

Step1: Multiply the first two terms

We have \(1\times10^{6}\text{ g solution} \times \frac{1\text{ mL}}{1.01\text{ g}}\). The grams unit cancels out, and we get \(\frac{1\times10^{6}\text{ mL}}{1.01}\).

Step2: Multiply by the third term

Now multiply by \(\frac{10^{-3}\text{ L}}{1\text{ mL}}\). The milliliters unit cancels out. So we calculate \(\frac{1\times10^{6}}{1.01}\times10^{-3}\text{ L}\).
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), \(1\times10^{6}\times10^{-3}=1\times10^{6-3}=1\times10^{3}\).
Then divide by \(1.01\): \(\frac{1\times10^{3}}{1.01}\approx990.099\text{ L}\) (or more precisely \(\frac{1000}{1.01}\text{ L}\))

Answer:

\(\approx 990.1\text{ L}\) (or \(\frac{1000}{1.01}\text{ L}\) which is approximately \(990.1\) liters)