The sun generates about 4×10^26

Question

joules of energy every second. There are about 3.15×1067
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)

Answer 1

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

Given:

• Energy generated by the Sun per second = \( 4 \times 10^{26} \) joules
• Number of seconds in a year = \( 3.15 \times 10^{67} \)

Now, we perform the multiplication:

\[ \text{Total energy in a year} = (4 \times 10^{26}) \times (3.15 \times 10^{67}) \]

We can multiply the coefficients and the powers of ten separately:

\[ = 4 \times 3.15 \times 10^{26 + 67} \]

Calculating the coefficients:

\[ 4 \times 3.15 = 12.6 \]

Now, we combine the powers of ten:

\[ 10^{26 + 67} = 10^{93} \]

So, we have:

\[ \text{Total energy in a year} = 12.6 \times 10^{93} \]

Next, we express \( 12.6 \) in scientific notation:

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

Thus, we rewrite the expression:

\[ 12.6 \times 10^{93} = 1.26 \times 10^{1} \times 10^{93} = 1.26 \times 10^{94} \]

Therefore, the total amount of energy the Sun generates in a year, expressed in scientific notation, is:

\[ \boxed{1.26 \times 10^{94}} \text{ joules} \]

Answer 2

are you sure the thing says your wrong sorry

Answer 3

Let’s recalculate the total energy the Sun generates in a year step by step to ensure accuracy.

1. The energy produced by the Sun per second is:

   \[ E = 4 \times 10^{26} \text{ joules/second} \]

2. The number of seconds in a year is approximately:

   \[ t = 3.15 \times 10^{67} \text{ seconds} \]

3. To find the total energy generated in a year, we multiply the energy per second by the number of seconds in a year:

   \[ \text{Total Energy} = E \times t = (4 \times 10^{26}) \times (3.15 \times 10^{67}) \]

4. We can multiply the coefficients and the powers of ten separately:

   • Multiplying the coefficients:

     \[ 4 \times 3.15 = 12.6 \]

   • Adding the exponents for the powers of ten:

     \[ 10^{26} \times 10^{67} = 10^{26 + 67} = 10^{93} \]

5. Combining these results, we have:

   \[ \text{Total Energy} = 12.6 \times 10^{93} \]

6. Now we convert \( 12.6 \) into proper scientific notation:

   \[ 12.6 = 1.26 \times 10^1 \]

   Therefore:

   \[ 12.6 \times 10^{93} = 1.26 \times 10^1 \times 10^{93} = 1.26 \times 10^{94} \]

Thus, the total energy the Sun generates in a year is:

\[ \boxed{1.26 \times 10^{94}} \text{ joules} \]

If there was any confusion or if there’s a specific part you want me to clarify, please let me know!