Question

The diameter of Mercury is approximately 4.9 × 10° kilometers.
The diameter of Saturn is approximately 1.2 x 105 kilometers
About how many times greater is the diameter of Saturn than the diameter of Mercury?
2.4
24
240
2400

Answer 1

To find out how many times greater the diameter of Saturn is than the diameter of Mercury, we need to divide the diameter of Saturn by the diameter of Mercury.

The diameter of Mercury is approximately \(4.9 \times 10^1\) kilometers (since \(4.9 \times 10^0\) is 4.9 and multiplying by \(10^1\) gives us 49 kilometers).

The diameter of Saturn is approximately \(1.2 \times 10^5\) kilometers.

Now, we can perform the calculation:

\[
\text{Ratio} = \frac{\text{Diameter of Saturn}}{\text{Diameter of Mercury}} = \frac{1.2 \times 10^5}{4.9 \times 10^1}
\]

To simplify this:

\[
\text{Ratio} = \frac{1.2}{4.9} \times \frac{10^5}{10^1} = \frac{1.2}{4.9} \times 10^{5-1} = \frac{1.2}{4.9} \times 10^4
\]

Calculating \(\frac{1.2}{4.9}\):

\[
\frac{1.2}{4.9} \approx 0.2449
\]

Now, multiplying by \(10^4\):

\[
0.2449 \times 10^4 \approx 2449
\]

Thus, the diameter of Saturn is approximately 2400 times greater than the diameter of Mercury.

So the answer is **2400**.