Question

what is the relationship between $8.76 \times 10^6$ and $8.76 \times 10^2$? select from the drop - down menus to correctly complete the statement. $8.76 \times 10^6$ is choose... times choose... than $8.76 \times 10^2$. (the drop - down options for the first choose... are 1000, 10,000, 100,000, 1,000,000)

Explanation:

Step1: Divide the two numbers

To find how many times \(8.76\times 10^{6}\) is of \(8.76\times 10^{2}\), we divide them: \(\frac{8.76\times 10^{6}}{8.76\times 10^{2}}\)

Step2: Simplify the coefficients and exponents

The \(8.76\) in the numerator and denominator cancels out. For the exponents, using the rule \(\frac{10^{a}}{10^{b}} = 10^{a - b}\), we have \(10^{6-2}=10^{4}\)

Step3: Calculate \(10^{4}\)

\(10^{4}=10000\)

Step4: Determine the relationship

Since \(8.76\times 10^{6}\) is larger than \(8.76\times 10^{2}\) (because the result of division is \(10000> 1\)), so \(8.76\times 10^{6}\) is \(10000\) times greater than \(8.76\times 10^{2}\)

Answer:

\(8.76\times 10^{6}\) is \(10000\) times greater than \(8.76\times 10^{2}\)