Question

The sun generates about 4×10 to the 26 power joules of energy every second there are about 3.15 times 10 to the seventh power seconds in a year, but how many joules of energy does the sun generate in a year write the answer in scientific notation

Answer 1

To find out how many joules of energy the sun generates in a year, you can multiply the energy generated per second by the number of seconds in a year.

The sun generates about \( 4 \times 10^{26} \) joules of energy every second, and there are approximately \( 3.15 \times 10^{7} \) seconds in a year.

\[
\text{Total energy} = \text{Energy per second} \times \text{Seconds in a year}
\]
\[
\text{Total energy} = (4 \times 10^{26} \, \text{joules/second}) \times (3.15 \times 10^{7} \, \text{seconds})
\]

Now, we can multiply the coefficients and add the exponents:

\[
= 4 \times 3.15 \times 10^{26} \times 10^{7}
\]
\[
= 12.6 \times 10^{33}
\]

To express \( 12.6 \) in proper scientific notation, we can rewrite \( 12.6 \) as \( 1.26 \times 10^{1} \):

\[
= 1.26 \times 10^{1} \times 10^{33} = 1.26 \times 10^{34}
\]

Thus, the total energy generated by the sun in a year is:

\[
\boxed{1.26 \times 10^{34}} \, \text{joules}
\]