Question

the sun releases $3.85 \times 10^{26}$ joules of energy every second. according to the e.i.a., the u.s. consumed about $1.03 \times 10^{20}$ 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: Separate Coefficients and Powers

We can rewrite the fraction $\frac{3.85\times10^{26}}{1.03\times10^{20}}$ as the product of two fractions: $\frac{3.85}{1.03}\times\frac{10^{26}}{10^{20}}$.

Step2: Divide the Coefficients

Calculate $\frac{3.85}{1.03}\approx3.7379$.

Step3: Divide the Powers of 10

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

Step4: Multiply the Results

Multiply the results from Step 2 and Step 3: $3.7379\times10^{6}=3737900$ (approximately).

Answer:

$\frac{3.85\times10^{26}}{1.03\times10^{20}}\approx3.74\times10^{6}$ (or approximately 3737864 when calculated more precisely)