To find out how many joules of energy the sun generates in a year, you need to multiply the energy generated in one second by the number of seconds in a year.
Given:
- The energy generated by the sun per second: \( 4 \times 10^{26} \) joules
- The number of seconds in a year: \( 3.15 \times 10^{7} \) seconds
Now, we can multiply these values together:
\[ (4 \times 10^{26}) \times (3.15 \times 10^{7}) \]
We can break this multiplication down:
- Multiply the coefficients: \(4 \times 3.15 = 12.6\)
- Multiply the powers of ten: \(10^{26} \times 10^{7} = 10^{(26 + 7)} = 10^{33}\)
So far, we have:
\[ 12.6 \times 10^{33} \]
Next, we need to express \(12.6\) in scientific notation. \(12.6\) can be expressed as \(1.26 \times 10^{1}\). Therefore:
\[ 12.6 \times 10^{33} = (1.26 \times 10^{1}) \times 10^{33} = 1.26 \times 10^{(1 + 33)} = 1.26 \times 10^{34} \]
Thus, the sun generates approximately:
\[ \boxed{1.26 \times 10^{34}} \text{ joules of energy in a year.} \]
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