To calculate the total energy generated by the sun in a year, you can multiply the energy generated per second by the number of seconds in a year.
Given:
- Energy generated by the sun per second = \(4 \times 10^{26}\) joules
- Seconds in a year = \(3.15 \times 10^{7}\)
Now, calculate the total energy generated in a year:
\[ \text{Total energy} = (\text{Energy per second}) \times (\text{Seconds in a year}) \] \[ \text{Total energy} = (4 \times 10^{26}) \times (3.15 \times 10^{7}) \]
To multiply these numbers, you can multiply the coefficients and then add the exponents of the powers of ten:
\[ 4 \times 3.15 = 12.6 \] \[ 10^{26} \times 10^{7} = 10^{(26 + 7)} = 10^{33} \]
So, \[ \text{Total energy} = 12.6 \times 10^{33} \]
Now, to express this in proper scientific notation, we need to express 12.6 as \(1.26 \times 10^1\):
\[ 12.6 \times 10^{33} = 1.26 \times 10^{34} \]
Thus, the total energy the sun generates in a year, expressed in scientific notation, is:
\[ \boxed{1.26 \times 10^{34}} \text{ joules} \]
1 answer