Dimensional Analysis problem

Question

The amount of fresh water on earth is estimated to be 3.73x10⁸km³. There are 1000L in a cubic meter. How many 20,000 gallon backyard swimming looks can you fill up with this volume of freshwater? (3.785 litres = 1 gallon)

Answer 1

1 km = 10³ m

So 1 km³ = (10³)³ m³ = 10⁹ m³ = 10¹² liters (using information in question)

SO 3.73 x 10⁸ km³

Multiply by 10¹² to convert to liters

Divide by 3.785 to convert to gallons

Divide by 20000 (gallons in 1 pool)

^{Answer :} 4.99339498 x 10^15

^{Precision ? Well the only data estimated here is 3.73 x 10^ 8}

^{This has 3 significant figures}

^{So we should quote our answer to 3 significant figures ie 4.99 x 10^15}

^Mike