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Math Operations with Scientific Notation

Subtract 4.31 x 10^-5 from 6.55 x 10^-4. Use the * to indicate the power of 2 points for the exponent.

Option 1: 6.11 x 10^-4
Option 2: 2.24 x 10^-5
Option 3: 2.24 x 10^-9
Option 4: 6.11 x 10^-9

1 Answer

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Final answer:

To subtract in scientific notation, align the exponents, perform the subtraction, and convert back into proper scientific notation. The correct answer is 6.11 x 10^-4 (Option 1).

Step-by-step explanation:

To subtract the numbers 4.31 x 10^-5 from 6.55 x 10^-4 in scientific notation, we need to make sure the exponents match. Since they do not match in this case, you'll first need to convert one of the numbers so that both have the same exponent. We will convert 6.55 x 10^-4 to the power of -5, by moving the decimal one place to the right, we get 65.5 x 10^-5.

Now we can subtract:

65.5 x 10^-5 - 4.31 x 10^-5 = (65.5 - 4.31) x 10^-5

Perform the subtraction:

65.5 - 4.31 = 61.19

So, 61.19 x 10^-5

However, we need to express this in proper scientific notation with only one non-zero digit to the left of the decimal point. So we adjust our number:

6.119 x 10^-4 (since we moved the decimal point one place to the left, we must increase the exponent by one to maintain the value).

Therefore, the correct answer and the option that reflects proper scientific notation is 6.11 x 10^-4, which is Option 1.

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