Question

The distance between Earth and the sun is approximately 150 million kilometres and between Uranus and the sun is approximately 3 billion kilometres.
Thus, the distance between Uranus and the sun is ___ times the distance between Earth and the sun.

• A. 0.5
• B. 2
• C. 20
• D. 200

Answer 1

The correct option is C 20

$\text{150 million kilometres}=150\times {10}^6\text{km}$

$\text{3 billion kilometres}=3\times {10}^9\text{km}$

$\therefore \frac{\text{Distance between Uranus and the sun}}{\text{Distance between Earth and the sun}}$
$=\frac{3\times {10}^9}{150\times {10}^6}=\frac{3\times {10}^9}{15\times 10\times {10}^6}=\frac{3\times {10}^9}{15\times {10}^7}(\because a^m\times a^n=a^{m+n})=0.2\times {10}^2(\because \frac{a^m}{a^n}=a^{m-n})=20$
Hence, the distance between Uranus and the sun is 20 times the distance between Earth and the sun.