Question

The sun generates about 4*10 to the power of 26 joules of energy every second there are about 3.15*10 to the power of 7 seconds in a year about how many joules of energy does the sun generate in a year write the answer in scientific notation

Answer 1

To find out how much energy the Sun generates in a year, you can multiply the energy it generates per second by the number of seconds in a year.

The energy generated by the Sun every second is \(4 \times 10^{26}\) joules, and the number of seconds in a year is approximately \(3.15 \times 10^{7}\).

So, you calculate:

\[
\text{Energy in a year} = \text{Energy per second} \times \text{Seconds in a year}
\]

\[
\text{Energy in a year} = (4 \times 10^{26} \, \text{J/s}) \times (3.15 \times 10^{7} \, \text{s})
\]

To multiply these two numbers in scientific notation:

1. Multiply the coefficients (the numbers in front):
\[
4 \times 3.15 = 12.6
\]

2. Add the exponents:
\[
10^{26} \times 10^{7} = 10^{(26 + 7)} = 10^{33}
\]

So, the combined result before converting to proper scientific notation is:

\[
12.6 \times 10^{33}
\]

Now, we need to rewrite \(12.6\) in proper scientific notation. Since \(12.6\) can be expressed as \(1.26 \times 10^{1}\), we can write it as:

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

Thus, the total energy generated by the Sun in a year, in scientific notation, is approximately:

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