To find out how many joules of energy the sun generates in a year, you can multiply the energy it generates every second by the number of seconds in a year.
Given:
- Energy generated per second by the sun: \( 4 \times 10^{26} \) joules
- Number of seconds in a year: \( 3.15 \times 10^{7} \) seconds
Now, calculate the total energy generated in one year:
\[ \text{Total energy} = \text{Energy per second} \times \text{Number of seconds in a year} \] \[ \text{Total energy} = (4 \times 10^{26}) \times (3.15 \times 10^{7}) \]
Now, perform the multiplication:
-
Multiply the coefficients: \[ 4 \times 3.15 = 12.6 \]
-
Multiply the powers of ten: \[ 10^{26} \times 10^{7} = 10^{(26+7)} = 10^{33} \]
Putting it all together:
\[ \text{Total energy} = 12.6 \times 10^{33} \]
Now, convert \( 12.6 \) to scientific notation:
\[ 12.6 = 1.26 \times 10^{1} \]
So the total energy is:
\[ 1.26 \times 10^{1} \times 10^{33} = 1.26 \times 10^{34} \]
Thus, the total energy generated by the sun in one year is:
\[ \boxed{1.26 \times 10^{34}} \] joules.