Question

the planet mercury is approximately 6×10⁷ kilometers from the sun. the planet neptune is approximately 4.5×10⁹ kilometers from the sun.
how many times farther from the sun is neptune than mercury?

Explanation:

Step1: Identify the formula

To find how many times farther Neptune is from the Sun than Mercury, we use the formula: \(\text{Ratio} = \frac{\text{Distance of Neptune}}{\text{Distance of Mercury}}\)

Given, Distance of Mercury \(= 6\times10^{7}\) km, Distance of Neptune \(= 4.5\times10^{9}\) km.

Step2: Substitute the values

Substitute the values into the formula: \(\text{Ratio} = \frac{4.5\times10^{9}}{6\times10^{7}}\)

Step3: Simplify the coefficients and exponents separately

First, simplify the coefficients: \(\frac{4.5}{6}= 0.75\)

Then, simplify the exponents using the rule \(\frac{10^{a}}{10^{b}} = 10^{a - b}\): \(\frac{10^{9}}{10^{7}}=10^{9 - 7}=10^{2} = 100\)

Step4: Multiply the results

Multiply the coefficient result with the exponent result: \(0.75\times100 = 75\)

Answer:

75