Question

A distance of 5.1 x 10 ^4
miles is how many times greater than a distance of 1.7 x 10 ^-2
miles?

Answer 1

To determine how many times greater a distance of \( 5.1 \times 10^4 \) miles is than a distance of \( 1.7 \times 10^{-2} \) miles, we can set up the following calculation:

\[
\text{Factor} = \frac{5.1 \times 10^4}{1.7 \times 10^{-2}}
\]

Now, we can simplify this expression:

\[
\text{Factor} = \frac{5.1}{1.7} \times \frac{10^4}{10^{-2}}
\]

Calculating \( \frac{5.1}{1.7} \):

\[
\frac{5.1}{1.7} \approx 3
\]

Now, calculating \( \frac{10^4}{10^{-2}} \):

\[
\frac{10^4}{10^{-2}} = 10^{4 - (-2)} = 10^{4 + 2} = 10^6
\]

Putting it all together, we get:

\[
\text{Factor} \approx 3 \times 10^6
\]

Thus, \( 5.1 \times 10^4 \) miles is approximately \( 3 \times 10^6 \) times greater than \( 1.7 \times 10^{-2} \) miles.