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.
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.
To find 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.
Given:
Energy generated per second = 4 × 10²⁶ joules
Number of seconds in a year = 3.15 × 10⁷ seconds
To calculate the total energy generated in a year:
Total energy generated = (energy generated per second) × (number of seconds in a year)
Substituting the given values:
Total energy generated = (4 × 10²⁶ joules) × (3.15 × 10⁷ seconds)
To multiply the numbers in scientific notation, we can multiply the coefficients and add the exponents:
Total energy generated = 4 × 3.15 × 10²⁶ × 10⁷ joules
Multiplying the coefficients: 4 × 3.15 = 12.6
Adding the exponents: 26 + 7 = 33
The total energy generated by the sun in a year is 12.6 × 10³³ joules.
Expressing the answer in scientific notation: 1.26 × 10³⁴ joules.
To find out how many joules of energy the sun generates in a year, we need to multiply the energy generated by the sun in one second by the number of seconds in a year.
Given:
Energy generated by the sun per second = 4 × 10²⁶ joules
Number of seconds in a year = 3.15 × 10⁷ seconds
To multiply these two values, we can simply multiply the numbers and add the exponents:
(4 × 10²⁶ joules) × (3.15 × 10⁷ seconds)
Multiplying the numbers: 4 × 3.15 = 12.6
Adding the exponents: 10²⁶ + 10⁷ = 10³³
Therefore, the sun generates approximately 12.6 × 10³³ joules of energy in a year. This can be expressed in scientific notation as 1.26 × 10³⁴ joules.