Question

1. (5pts) the andromeda galaxy is a distance of about 2.5×10^6 light - years from earth. using that one light - year is about 9.5×10^15 m, how many femtometers (fm) is the distance to andromeda if 1 fm = 10^(-15) m?

Explanation:

Step1: First find the distance in meters

The distance to Andromeda in meters is $d = 2.5\times10^{6}\times9.5\times 10^{15}\text{ m}$ (since 1 light - year is about $9.5\times 10^{15}\text{ m}$ and the distance is $2.5\times10^{6}$ light - years).
Using the rule of exponents $a^m\times a^n=a^{m + n}$, we have $d=(2.5\times9.5)\times10^{6 + 15}\text{ m}=23.75\times10^{21}\text{ m}=2.375\times 10^{22}\text{ m}$.

Step2: Then convert to femtometers

Since $1\text{ fm}=10^{- 15}\text{ m}$, then the number of femtometers $N=\frac{d}{10^{-15}}$.
Substitute $d = 2.375\times 10^{22}\text{ m}$ into the formula: $N=\frac{2.375\times 10^{22}}{10^{-15}}$.
Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we get $N = 2.375\times10^{22-(-15)}=2.375\times 10^{37}\text{ fm}$.

Answer:

$2.375\times 10^{37}$ fm