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Approximately how many times greater is [tex]$5 \times 10^8$[/tex] than [tex]$8 \times 10^5$[/tex]?

A. 62.5
B. 625
C. 6250
D. 625,000

Answer :

To determine how many times greater [tex]\(5 \times 10^8\)[/tex] is than [tex]\(8 \times 10^5\)[/tex], we can follow these steps:

1. Write down the numbers in standard form:
- [tex]\(5 \times 10^8 = 500,000,000\)[/tex]
- [tex]\(8 \times 10^5 = 800,000\)[/tex]

2. Perform a division to compare the sizes of the two numbers:
[tex]\[
\frac{5 \times 10^8}{8 \times 10^5}
\][/tex]

3. Simplify the division:
- Divide the coefficients: [tex]\(\frac{5}{8}\)[/tex]
- Subtract the exponents: [tex]\(10^{(8-5)} = 10^3\)[/tex]

So it becomes:
[tex]\[
\frac{5}{8} \times 10^3
\][/tex]

4. Calculate each part:
- [tex]\(\frac{5}{8} = 0.625\)[/tex]
- [tex]\(10^3 = 1000\)[/tex]

5. Multiply the results:
[tex]\[
0.625 \times 1000 = 625
\][/tex]

Thus, [tex]\(5 \times 10^8\)[/tex] is 625 times greater than [tex]\(8 \times 10^5\)[/tex].

Therefore, the answer is [tex]\(625\)[/tex].

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