Question

8.03x10^-8 2.56x10^-2
subtract the numbers above. show your work below

Answer 1

how do you turn 2.56x10^-2 exponent into 10^-8

Answer 2

simpler

Answer 3

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

1. **Identify the exponents**: The first number has an exponent of -8 and the second has an exponent of -2. The larger exponent is -2, so we will convert the first number to have the same exponent.

2. **Convert \( 8.03 \times 10^{-8} \) to the same exponent as \( 2.56 \times 10^{-2} \)**:
\[
8.03 \times 10^{-8} = 8.03 \times 10^{-8 + 6} = 8.03 \times 0.000001 = 8.03 \times 10^{-8 + 6} = 0.0000000803 = 8.03 \times 10^{-8} = 0.0000000803
\]
\[
= 0.0000000803 = 0.00000008 + 0.00000803 \text{(not needed)}
\]

We can rewrite it with the exponent of -2:
\[
8.03 \times 10^{-8} = 0.0000803 \text{or } 8.03 \times 10^{-8} = 0.0000000803
\]

Now, we can convert it to:
\[
8.03 \times 10^{-8} = 0.0000000803 \times 10^{-6} \text{ and move the decimal 6 places left.}
\]

Which means:
\[
8.03 \times 10^{-8} = 8.03 \times 10^{-8 + 6} = 8.03 \times 10^{-2} \times 10^{-6} = 0.0000008003 = 0.0000000803
\]

So we can compare 8.03 \text{to } 2.56 \times 10^{-2}
3. **Perform the subtraction**: We can write it as:
\[
- 2.56 \times 10^{-2} \text{ (which is equal to } - 0.0000256)
\]

Substituting, we have the same exponent:
\[
= (0.0000000803 - 0.0000256) \\
\]

We will also express this appropriately:
\[
0.0000000803 - 0.0000256= -0.0000255197
\]

So, reorganizing would state it as:

4. **Final answer**: The result of the subtraction will be approximately equal to:
\[
-2.56000 \text{ or } -2.55617 = -2.56 \text{ or } -0.0000255197
\]

Thus, the final answer is approximately:
\[
\mathbf{-2.5600000000 \times 10^{-2}}
\]

Answer 4

To express \( 2.56 \times 10^{-2} \) with an exponent of \( 10^{-8} \), you need to convert the base while adjusting the coefficient accordingly. Here's how to do it step by step:

1. **Identify the change in the exponent**:
- You want to change from \( 10^{-2} \) to \( 10^{-8} \).
- To do this, you need to reduce the exponent by \( -2 - (-8) = 6 \).

2. **Adjust the coefficient**:
- Every time you decrease the exponent by 1, you multiply the coefficient by 10.
- Since you are reducing it by 6, you will multiply the coefficient \( 2.56 \) by \( 10^6 \):
\[
2.56 \times 10^{-2} = 2.56 \times 10^{6} \times 10^{-8}.
\]

3. **Combine the terms**:
- Now, rewriting this gives:
\[
= 2.56 \times 10^6 \text{ inside is } \div 1000000 (10^6 )
\]

Thus,
\[
= 2.56 \times 10^{-2} = 2.56 \cdot 10^6 \cdot 10^{-8} = 0.0000256
\]

4. **Final expression**:
- So, now you can express it as:
\[
2.56 \times 10^{-2} = 2.56 \times 10^{-8} \times 10^6.
\]

So the form of \( 2.56 \times 10^{-2} \) expressed with an exponent of \( 10^{-8} \) becomes:
\[
2.56 \times 10^{-2} = 2.56 \times 10^{-8} \times 10^6 = 25.6 \times 10^{-8}.
\]

This is the correct transformation for the value. In scientific notation, the coefficient of \( 25.6 \) might further be adjusted as \( 2.56 \times 10^{-7} \).

In summary, you convert \( 2.56 \times 10^{-2} \) into \( 25.6 \times 10^{-8}\) or as \( 2.56 \times 10^{-7}\).

Answer 5

Sure! Here’s a simpler step-by-step explanation to convert \( 2.56 \times 10^{-2} \) into a form with an exponent of \( 10^{-8} \):

1. **Identify how to change the exponent**:
- You want to change \( 10^{-2} \) to \( 10^{-8} \), which means you're going to decrease the exponent by 6 (since \(-2 - (-8) = 6\)).

2. **Adjust the coefficient**:
- When you decrease the exponent by 6, you need to multiply the coefficient \( 2.56 \) by \( 10^6\) (because every decrease in exponent by 1 means you multiply the coefficient by 10):
\[
2.56 \times 10^{-2} = 2.56 \times 10^{6} \times 10^{-8}
\]

3. **Combine the coefficients**:
- Multiply the coefficient by \( 10^6 \):
\[
= 2.56 \times 10^{6} \times 10^{-8} = 25.6 \times 10^{-8}
\]

So, you can express \( 2.56 \times 10^{-2} \) with an exponent of \( 10^{-8} \) as:
\[
25.6 \times 10^{-8}
\]

Or, to write it in proper scientific notation:
\[
2.56 \times 10^{-7}
\]

This is how you convert \( 2.56 \times 10^{-2} \) into a format with \( 10^{-8} \).