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Chapter 4: Problem 23

Write each number in scientific notation. $$42.5 \times 10^{2}$$

Short Answer

Expert verified
The number \(42.5 \times 10^{2}\) written in scientific notation is \(4.25 \times 10^{3}\).

Step by step solution

01

Identify the number

Identify the number that we need to convert into scientific notation, which is \(42.5 \times 10^{2}\).
02

Rewriting the number

The given number is already partly in scientific notation, but the \(m\) part is not within the required range of 1 through 10. To fit our number into this form, we need to rewrite \(42.5\) as \(4.25 \times 10^1\). This does not change the value of the number, due to the property of exponents that says \(a^{m+n} = a^m \times a^n\).
03

Final output

Now multiply the original exponent \(10^{2}\) with the new exponent \(10^{1}\). This equates to \(10^{2+1}\), or \(10^{3}\). Thus, the final scientific notation of the given number would be \(4.25 \times 10^{3}\).

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