The sun generates about 4×10^26 joules of energy every second. There are about 3.15×10^7 seconds in a year. About how many joules of energy does the sun generate in a year? Write the answer in scientific notation. Express the answer to the exact decimal place.(1 point)

Answer 1

To find the total energy the sun generates in a year, we can multiply the energy generated per second by the number of seconds in a year:

\[ \text{Energy per year} = (\text{Energy per second}) \times (\text{Seconds per year}) \]

Given:

• Energy per second = \(4 \times 10^{26}\) joules
• Seconds per year = \(3.15 \times 10^{7}\) seconds

Now, let's calculate:

\[ \text{Energy per year} = (4 \times 10^{26}) \times (3.15 \times 10^{7}) \]

We can multiply the coefficients (4 and 3.15) and add the exponents of 10:

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

Now, we combine these results:

\[ \text{Energy per year} = 12.6 \times 10^{33} \]

To express this in proper scientific notation, we need to convert \(12.6\) into \(1.26\) (since we keep only one non-zero digit to the left of the decimal) and increase the exponent of 10 by 1:

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

Therefore, the total energy the sun generates in a year is:

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