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 distance in meters

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

Step2: Then convert to femtometers

Given 1 fm = $10^{-15}$ m, let the distance in femtometers be $d_{fm}$. We know that $d_{fm}=\frac{d_m}{10^{-15}}$. Substituting $d_m = 2.375\times10^{22}$ m into the formula, we get $d_{fm}=2.375\times10^{22}\div10^{-15}$. Using the rule of exponents $\frac{a^m}{a^n}=a^{m - n}$, we have $d_{fm}=2.375\times10^{22-(-15)}=2.375\times10^{37}$ fm.

Answer:

$2.375\times10^{37}$ fm