without any equipment, you can see stars that are 2,800,000 light - years away. by looking through a small…

without any equipment, you can see stars that are 2,800,000 light - years away. by looking through a small telescope, you can see stars that are 3,112,000,000 light - years away. approximately how many times as far can you see using a small telescope as without any equipment? choose 1 answer: a 1·10² b 3·10² c 1·10³ d 3·10³

without any equipment, you can see stars that are 2,800,000 light - years away. by looking through a small telescope, you can see stars that are 3,112,000,000 light - years away. approximately how many times as far can you see using a small telescope as without any equipment? choose 1 answer: a 1·10² b 3·10² c 1·10³ d 3·10³

Answer

Explanation:

Step1: Write numbers in scientific - notation

The distance of stars seen without equipment is $d_1 = 2800000=2.8\times 10^{6}$ light - years. The distance of stars seen with a small telescope is $d_2 = 3112000000 = 3.112\times 10^{9}$ light - years.

Step2: Calculate the ratio

The ratio $r=\frac{d_2}{d_1}=\frac{3.112\times 10^{9}}{2.8\times 10^{6}}$. Using the rule of exponents $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $\frac{3.112}{2.8}\times10^{9 - 6}$. $\frac{3.112}{2.8}\approx1.11$, and $1.11\times10^{3}\approx1\times10^{3}$.

Answer:

C. $1\cdot10^{3}$