Question
Writing Subtract 5.8 times 10 Superscript 4 Baseline minus 8 times 10 cubed. Use pencil and paper. Describe the process of rewriting the numbers in this problem with the same power of 10.
Answers
GPT-4o mini
To subtract \(5.8 \times 10^4\) and \(8 \times 10^3\), you need to rewrite both numbers with the same power of 10. Here’s how to do that step by step:
1. **Identify the exponents**:
You have \(10^4\) and \(10^3\). Since \(10^4\) is a higher power than \(10^3\), we will rewrite \(8 \times 10^3\) to have the same exponent as \(5.8 \times 10^4\).
2. **Rewrite \(8 \times 10^3\)**:
To convert \(8 \times 10^3\) to a similar base of \(10^4\):
- We can express \(8 \times 10^3\) as \(8 \times 10^{3} = 8 \times 10^{3} \times \frac{10^1}{10^1} = 8 \times 10^{4 - 1} = 8 \times \frac{10^4}{10} = \frac{8 \times 10^4}{10} = 0.8 \times 10^4\).
3. **Rewrite the equation**:
Now that both terms are expressed in terms of \(10^4\), we can rewrite the subtraction as:
\[
5.8 \times 10^4 - 0.8 \times 10^4
\]
4. **Combine the terms**:
Since we have the same power of 10, we can combine the coefficients:
\[
(5.8 - 0.8) \times 10^4 = 5.0 \times 10^4
\]
5. **Final result**:
Therefore, \(5.8 \times 10^4 - 8 \times 10^3\) simplifies to:
\[
5.0 \times 10^4
\]
In summary, the process involved rewriting \(8 \times 10^3\) as \(0.8 \times 10^4\) to match the exponent of \(10^4\), allowing for straightforward subtraction of the coefficients.
1. **Identify the exponents**:
You have \(10^4\) and \(10^3\). Since \(10^4\) is a higher power than \(10^3\), we will rewrite \(8 \times 10^3\) to have the same exponent as \(5.8 \times 10^4\).
2. **Rewrite \(8 \times 10^3\)**:
To convert \(8 \times 10^3\) to a similar base of \(10^4\):
- We can express \(8 \times 10^3\) as \(8 \times 10^{3} = 8 \times 10^{3} \times \frac{10^1}{10^1} = 8 \times 10^{4 - 1} = 8 \times \frac{10^4}{10} = \frac{8 \times 10^4}{10} = 0.8 \times 10^4\).
3. **Rewrite the equation**:
Now that both terms are expressed in terms of \(10^4\), we can rewrite the subtraction as:
\[
5.8 \times 10^4 - 0.8 \times 10^4
\]
4. **Combine the terms**:
Since we have the same power of 10, we can combine the coefficients:
\[
(5.8 - 0.8) \times 10^4 = 5.0 \times 10^4
\]
5. **Final result**:
Therefore, \(5.8 \times 10^4 - 8 \times 10^3\) simplifies to:
\[
5.0 \times 10^4
\]
In summary, the process involved rewriting \(8 \times 10^3\) as \(0.8 \times 10^4\) to match the exponent of \(10^4\), allowing for straightforward subtraction of the coefficients.