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8.03x10^-8 2.56x10^-2

subtract the numbers above. show your work below

5 answers

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:

  1. 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: \[ \mathbf{-2.5600000000 \times 10^{-2}} \]

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

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 \( 2.56 \times 10^{-7}\).

simpler

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 \( 10^{-8} \).