Multiply in Scientific Notation Practice

Question

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Question
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.(1 point)
joules
Remaining Attempts : 3
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Answer 1

To find out how many joules of energy the sun generates in a year, we can multiply the energy generated per second by the number of seconds in a year.

Given:

• Energy per second = \( 4 \times 10^{26} \) joules/second
• Seconds in a year = \( 3.15 \times 10^{7} \) seconds

Now, we can perform the multiplication:

\[ (4 \times 10^{26}) \times (3.15 \times 10^{7}) = 4 \times 3.15 \times 10^{26 + 7} \]

Calculating \( 4 \times 3.15 \):

\[ 4 \times 3.15 = 12.6 \]

Now we find the power of ten:

\[ 10^{26 + 7} = 10^{33} \]

Putting it all together:

\[ 12.6 \times 10^{33} \]

Now, we want to express \( 12.6 \) in scientific notation. Since \( 12.6 = 1.26 \times 10^{1} \), we can rewrite the entire expression:

\[ 12.6 \times 10^{33} = 1.26 \times 10^{1} \times 10^{33} = 1.26 \times 10^{34} \]

Therefore, the sun generates approximately

\[ \boxed{1.26 \times 10^{34}} \]

joules of energy in a year.