Question

evaluate. express your answer in scientific notation. \\(9.54 \times 10^4 - 8,710\\)

Explanation:

Step1: Convert \(8710\) to scientific notation

To subtract, we first convert \(8710\) to scientific notation. We know that \(8710 = 8.71\times10^{3}\), but we can also write \(9.54\times 10^{4}\) as \(95.4\times 10^{3}\) (since \(10^{4}=10\times10^{3}\), so \(9.54\times10\times 10^{3}=95.4\times 10^{3}\)) to have the same exponent of 10 for both terms.

Step2: Subtract the two numbers

Now we subtract \(8710 = 8.71\times 10^{3}\) (or \(8.71\times10^{3}\)) from \(9.54\times 10^{4}=95.4\times 10^{3}\). So \(95.4\times 10^{3}- 8.71\times 10^{3}=(95.4 - 8.71)\times10^{3}\)
Calculate \(95.4-8.71 = 86.69\)
Now we need to convert \(86.69\times 10^{3}\) to scientific notation. We know that scientific notation is of the form \(a\times10^{n}\) where \(1\leqslant a< 10\). So we rewrite \(86.69\times 10^{3}\) as \(8.669\times 10^{4}\) (because \(86.69 = 8.669\times 10^{1}\), so \(8.669\times 10^{1}\times10^{3}=8.669\times 10^{4}\))

Answer:

\(8.669\times 10^{4}\)