8.03x10^-8 2.56x10^-2

Question

subtract the numbers above. show your work below

Answer 1

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: $$\mathbf{-}\mathbf{2.5600000000}\times {\mathbf{10}}^{\mathbf{-}\mathbf{2}}$$

Answer 2

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

Answer 3

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: $$=2.56\times {10}^6\text{ inside is }÷1000000({10}^6)$$

   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 4

simpler

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 ${10}^{-8}$.