Question

Writing  Subtract 4.1 times 10 Superscript 5 Baseline minus 8 times 10 Superscript 4. Use pencil and paper. Describe the process of rewriting the numbers in this problem with the same power of 10.
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Part 1
4.1 times 10 Superscript 5 Baseline minus 8 times 10 Superscript 4equals
  
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​(Use scientific notation. Use the multiplication symbol in the math palette as​ needed.)

Answer 1

To subtract \( 4.1 \times 10^5 \) and \( 8 \times 10^4 \), you'll want to rewrite both numbers with the same power of 10. Here’s how to do it step by step:

1. **Identify the Powers of 10**:
- The first number is \( 4.1 \times 10^5 \).
- The second number is \( 8 \times 10^4 \).

2. **Convert the Second Number**:
- You want to convert \( 8 \times 10^4 \) to a power of \( 10^5 \). To do this, you can multiply by \( 10^1 \) (which is equal to 10) to adjust it:
\[
8 \times 10^4 = 8 \times 10^4 \times \frac{10}{10} = 8 \times 10^{4+1} = 8 \times 10^5 \times 0.1 = 0.8 \times 10^5
\]
This operation allows you to express \( 8 \times 10^4 \) as \( 0.8 \times 10^5 \).

3. **Now Rewrite the Problem**:
- We can rewrite the original problem as:
\[
4.1 \times 10^5 - 0.8 \times 10^5
\]

4. **Perform the Subtraction**:
- Since both terms are now expressed with the same power of 10, you can subtract the coefficients:
\[
(4.1 - 0.8) \times 10^5 = 3.3 \times 10^5
\]

5. **Final Result**:
\[
4.1 \times 10^5 - 8 \times 10^4 = 3.3 \times 10^5
\]

So, the final answer in scientific notation is:
\[
\boxed{3.3 \times 10^5}
\]