Powers of 10 can be helpful for making calculations with large or small numbers. For example, in 2014, the United States had

318,586,495

people who used the equivalent of

2,203,799,778,107

kilograms of oil in energy. The amount of energy per person is the total energy divided by the total number of people. We can use powers of 10 to estimate the total energy as $$2 \boldcdot 10^{12}$$ and the population as $$3 \boldcdot 10^8$$ So the amount of energy per person in the U.S. is roughly $$2 \boldcdot 10^{12} \div 3 \boldcdot 10^8$$ That is the equivalent of $$\frac{2}{3} \boldcdot 10^4$$ kilograms of oil in energy. That’s a lot of energy—the equivalent of almost 7,000 kilograms of oil per person!

In general, when we want to perform arithmetic with very large or small quantities, estimating with powers of 10 and using exponent rules can help simplify the process. If we wanted to find the exact quotient of 2,203,799,778,107 by 318,586,495, then using powers of 10 would not simplify the calculation.