Question
256.7 x 10^12. Show your work
Answers
GPT-4o mini
To express \( 256.7 \times 10^{12} \) in standard form, you can follow these steps:
1. **Recognize the structure**: The number \( 256.7 \) is already in decimal form. The \(10^{12}\) indicates that we will be moving the decimal point 12 places to the right.
2. **Moving the decimal point**: Start with the number \( 256.7 \) and move the decimal point 12 places to the right.
- Moving it 3 places to the right transforms \( 256.7 \) into \( 2567000 \).
- Continuing to move it further, you will need to append zeros to fill in the additional places.
3. **Final counting**:
- After moving the decimal 3 places, you have \( 2567000 \).
- You need to move it 9 more places to reach a total of 12, which means you will add 9 zeros after \( 2567000 \).
So, we have:
\[
256.7 \times 10^{12} = 256700000000000
\]
Putting it all together, the final answer in standard form is:
\[
\boxed{256700000000000}
\]
1. **Recognize the structure**: The number \( 256.7 \) is already in decimal form. The \(10^{12}\) indicates that we will be moving the decimal point 12 places to the right.
2. **Moving the decimal point**: Start with the number \( 256.7 \) and move the decimal point 12 places to the right.
- Moving it 3 places to the right transforms \( 256.7 \) into \( 2567000 \).
- Continuing to move it further, you will need to append zeros to fill in the additional places.
3. **Final counting**:
- After moving the decimal 3 places, you have \( 2567000 \).
- You need to move it 9 more places to reach a total of 12, which means you will add 9 zeros after \( 2567000 \).
So, we have:
\[
256.7 \times 10^{12} = 256700000000000
\]
Putting it all together, the final answer in standard form is:
\[
\boxed{256700000000000}
\]