To find out how many times farther Neptune is from the Sun compared to Mercury, we can divide the distance from the Sun to Neptune by the distance from the Sun to Mercury.
Given:
- Distance to Neptune: \( 4.5 \times 10^9 \) kilometers
- Distance to Mercury: \( 5.79 \times 10^7 \) kilometers
Now we perform the division:
\[ \text{Distance Ratio} = \frac{\text{Distance to Neptune}}{\text{Distance to Mercury}} = \frac{4.5 \times 10^9}{5.79 \times 10^7} \]
To simplify this, we can express it as:
\[ \frac{4.5}{5.79} \times \frac{10^9}{10^7} = \frac{4.5}{5.79} \times 10^{9-7} = \frac{4.5}{5.79} \times 10^2 \]
Calculating \( \frac{4.5}{5.79} \):
\[ \frac{4.5}{5.79} \approx 0.776 \]
Now we multiply this result by \( 10^2 \):
\[ 0.776 \times 100 = 77.6 \]
Therefore, rounding to the nearest tenth, Neptune is approximately:
\[ \boxed{77.6} \]
times farther from the sun than Mercury.