The sun generates about 4×1026 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.
To find the total amount of energy the sun generates in a year, we multiply the amount of energy generated per second by the number of seconds in a year.
Total energy generated in a year = (4×10^26 joules/second) × (3.15×10^7 seconds/year)
To multiply the numbers in scientific notation, we multiply the coefficients and add the exponents.
Total energy generated in a year = 4×3.15×10^(26+7) joules
= 12.6×10^33 joules
Since the coefficient is less than 10, we express it as 1.26 and adjust the exponent.
Total energy generated in a year = 1.26×10^34 joules
To find the total energy generated by the sun in a year, we multiply the energy generated per second by the number of seconds in a year.
Energy generated per second: 4 × 10^26 joules
Number of seconds in a year: 3.15 × 10^7 seconds
Multiplying these two values gives us:
(4 × 10^26 joules) × (3.15 × 10^7 seconds) = 12.6 × 10^33 joules
Since the answer should be in scientific notation, we can rewrite 12.6 x 10^33 as:
1.26 × 10^(34)
Therefore, the sun generates approximately 1.26 × 10^34 joules of energy in a year.
To calculate the amount of energy the sun generates in a year, we need to multiply the energy generated per second by the number of seconds in a year. Let's break down the calculation step by step:
1. Energy generated per second: 4×10^26 J/second
2. Number of seconds in a year: 3.15×10^7 seconds/year
To calculate the energy generated in a year, we multiply these two numbers:
Energy generated in a year = (4×10^26 J/second) × (3.15×10^7 seconds/year)
To multiply these scientific notations, we need to multiply the coefficients (4 and 3.15) and add the exponents (26 + 7):
Energy generated in a year = (4 × 3.15) × 10^(26 + 7) J
Calculating the multiplication of coefficients gives:
Energy generated in a year = 12.6 × 10^33 J
The answer in scientific notation, expressing the exact decimal place, is:
1.26 × 10^34 J