The sun generates about 4 × 10²⁶ joules of 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 find the total energy generated by the sun in a year, we can multiply the energy generated per second by the number of seconds in a year:

4 × 10²⁶ joules/second * 3.15 × 10⁷ seconds/year.

Multiplying these two numbers together, we get:

(4 × 10²⁶) * (3.15 × 10⁷) = (4 * 3.15) × (10²⁶ * 10⁷) = 12.6 × 10^(26+7).

To express this answer in scientific notation, we need to convert it to the form A × 10^n, where A is a number between 1 and 10:

12.6 × 10^(26+7) = 12.6 × 10^(33).

Therefore, the sun generates approximately 1.26 × 10³⁴ joules of energy in a year.