Question

the sun releases 3.85×10²⁶ joules of energy every second. according to the e.i.a., the u.s. consumed about 1.03×10²⁰ joules of energy in 2011. if the u.s. continues at that rate of consumption, how many years could one second of energy from the sun power the u.s.? what is $\frac{(3.85\times 10^{26})}{(1.03\times 10^{20})}$?

Explanation:

Step1: Divide the coefficients

$\frac{3.85}{1.03}\approx3.74$

Step2: Divide the powers of 10

Using the rule $\frac{a^m}{a^n}=a^{m - n}$, we have $\frac{10^{26}}{10^{20}}=10^{26 - 20}=10^{6}$

Step3: Combine the results

The result of $\frac{3.85\times10^{26}}{1.03\times10^{20}}$ is $3.74\times10^{6}$ seconds.

Step4: Convert seconds to years

There are $60$ seconds in a minute, $60$ minutes in an hour, $24$ hours in a day and $365$ days in a year. So the number of seconds in a year is $60\times60\times24\times365 = 31536000=3.1536\times 10^{7}$ seconds.
Let $y$ be the number of years. Then $y=\frac{3.74\times10^{6}}{3.1536\times 10^{7}}\approx0.12$ years.

Answer:

$0.12$ years