Question

8.03 X 10-8
2.56 × 10-2
Subtract the numbers above. Show your work below.
For example: 2.3 X 10^3 + 1.7 X 10^3 = 4 X 10^3

Answer 1

To subtract the numbers \(8.03 \times 10^{-8}\) and \(2.56 \times 10^{-2}\), we first need to express them with the same exponent.

1. **Identify the smaller exponent**:
The smaller exponent is \(-8\).

2. **Convert \(2.56 \times 10^{-2}\) to the same exponent**:
\[
2.56 \times 10^{-2} = 2.56 \times 10^{-2 + 6} \times 10^{-6} = 2.56 \times 10^{4} \times 10^{-6}
\]
So,
\[
2.56 \times 10^{-2} = 256 \times 10^{-8}
\]

3. **Now we can rewrite our equation**:
\[
8.03 \times 10^{-8} - 256 \times 10^{-8}
\]

4. **Combine the numbers**:
\[
(8.03 - 256) \times 10^{-8} = -247.97 \times 10^{-8}
\]

5. **Express the answer in scientific notation**:
To convert \(-247.97\) to scientific notation, we move the decimal two places to the left:
\[
-247.97 \times 10^{-8} = -2.4797 \times 10^{-6}
\]

6. **Final answer**:
\[
8.03 \times 10^{-8} - 2.56 \times 10^{-2} = -2.4797 \times 10^{-6}
\]

So the final result is:
\[
-2.4797 \times 10^{-6}
\]

Answer 2

u sure

Answer 3

Let's double-check the calculations step-by-step to ensure accuracy.

We need to subtract \(8.03 \times 10^{-8}\) from \(2.56 \times 10^{-2}\).

1. **Numbers in scientific notation**:
- \(8.03 \times 10^{-8}\)
- \(2.56 \times 10^{-2}\)

2. **Convert both numbers to the same exponent**:
- The exponent \(-2\) from \(2.56 \times 10^{-2}\) is larger than \(-8\), so we will convert \(2.56 \times 10^{-2}\) to have an exponent of \(-8\).

Convert \(2.56 \times 10^{-2}\):
\[
2.56 \times 10^{-2} = 2.56 \times 10^{-2 + 6} \times 10^{-6} = 2.56 \times 10^{4} \times 10^{-6} = 25600 \times 10^{-6}
\]
So,
\[
2.56 \times 10^{-2} = 25600 \times 10^{-8}
\]

3. **Now we can subtract**:
Rewrite \(2.56 \times 10^{-2}\) back in terms of the same exponent:
\[
25600 \times 10^{-8} - 8.03 \times 10^{-8}
\]
Combine:
\[
(25600 - 8.03) \times 10^{-8} = 25591.97 \times 10^{-8}
\]

4. **Express in scientific notation**:
Move the decimal point two places left to convert \(25591.97\) into proper scientific notation:
\[
25591.97 \times 10^{-8} = 2.559197 \times 10^{-4}
\]

Therefore, the final answer is:
\[
2.559197 \times 10^{-4}
\]

Thank you for your patience, and I apologize for the earlier confusion!

Answer 4

estimate it

Answer 5

To estimate the subtraction of the two numbers \(8.03 \times 10^{-8}\) and \(2.56 \times 10^{-2}\), we can look at the leading factors and how they compare.

1. **Identify the orders of magnitude**:
- \(8.03 \times 10^{-8}\) is a very small number (in the order of \(10^{-8}\)).
- \(2.56 \times 10^{-2}\) is much larger (in the order of \(10^{-2}\)).

2. **Estimate the numbers**:
- You can round \(8.03 \times 10^{-8}\) to about \(8 \times 10^{-8}\).
- Round \(2.56 \times 10^{-2}\) to about \(2.6 \times 10^{-2}\).

3. **Subtraction**:
Since \(2.6 \times 10^{-2}\) is significantly larger than \(8 \times 10^{-8}\), we can say:
\[
2.6 \times 10^{-2} - 8 \times 10^{-8} \approx 2.6 \times 10^{-2}
\]
because \(8 \times 10^{-8}\) is negligible compared to \(2.6 \times 10^{-2}\).

4. **Final estimated result**:
Thus, an estimated result for the subtraction would be:
\[
\approx 2.6 \times 10^{-2}
\]

So, the approximate answer for the subtraction \(8.03 \times 10^{-8} - 2.56 \times 10^{-2}\) is \( \mathbf{2.6 \times 10^{-2}} \).