Question

how many times greater is the value $6 \times 10^8$ than the value 300? $3 \times 10^6$ $2 \times 10^4$ $3 \times 10^4$ $2 \times 10^6$

Explanation:

Step1: Rewrite 300 in scientific notation

To find how many times greater \(6\times10^{8}\) is than 300, we first rewrite 300 in scientific notation. 300 can be written as \(3\times10^{2}\) since \(3\times100 = 3\times10^{2}\).

Step2: Divide the two numbers

We divide \(6\times10^{8}\) by \(3\times10^{2}\) to find the multiple. Using the rule of exponents for division \(\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}\), we have \(\frac{6\times10^{8}}{3\times10^{2}}=\frac{6}{3}\times10^{8 - 2}\).

Step3: Simplify the expression

Simplify \(\frac{6}{3}=2\) and \(8 - 2 = 6\), so the result is \(2\times10^{6}\).

Answer:

\(2\times10^{6}\) (the fourth option: \(2\times10^{6}\))