The sun generates about 4 x 1026 joules of energy every second. There are about 3.15 × 107 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.

Answer 1

To calculate the total energy generated by the sun in a year, we need to multiply the energy generated per second by the number of seconds in a year.

1. The energy generated by the sun every second is: \[ 4 \times 10^{26} \text{ joules/second} \]

2. The number of seconds in a year is: \[ 3.15 \times 10^{7} \text{ seconds/year} \]

Now, we multiply these two values: \[ \text{Total energy in a year} = \text{Energy per second} \times \text{Seconds in a year} \] \[ = (4 \times 10^{26}) \times (3.15 \times 10^{7}) \]

We can multiply the coefficients (the numbers before the powers of ten) and then add the exponents (the powers of ten): \[ \text{Coefficients: } 4 \times 3.15 = 12.6 \]

\[ \text{Exponents: } 10^{26} \times 10^{7} = 10^{(26 + 7)} = 10^{33} \]

Now, combining these results: \[ \text{Total energy} = 12.6 \times 10^{33} \text{ joules} \]

To express this in proper scientific notation, we need to adjust \(12.6\) to \(1.26\) and increase the exponent by 1: \[ 12.6 \times 10^{33} = 1.26 \times 10^{34} \]

Therefore, the energy generated by the sun in a year, expressed in scientific notation, is: \[ \boxed{1.26 \times 10^{34}} \text{ joules} \]