Question

5.6 express one light - year in scientific notation in terms of a) nanometers b) giga - meters c) femtometers

Explanation:

Step1: Recall the definition of a light - year

A light - year is the distance that light travels in one year. The speed of light $c = 2.99792458\times10^{8}\ m/s$ and the number of seconds in a year $t=365\times24\times3600\ s = 3.1536\times 10^{7}\ s$. So, one light - year $d = c\times t=2.99792458\times10^{8}\times3.1536\times 10^{7}\ m=9.4607304725808\times 10^{15}\ m$.

Step2: Convert to nanometers

We know that $1\ m = 10^{9}\ nm$. So, $d_{nm}=9.4607304725808\times 10^{15}\times10^{9}\ nm = 9.4607304725808\times 10^{24}\ nm\approx9.46\times 10^{24}\ nm$.

Step3: Convert to gigameters

We know that $1\ Gm = 10^{9}\ m$. So, $d_{Gm}=\frac{9.4607304725808\times 10^{15}}{10^{9}}\ Gm=9.4607304725808\times 10^{6}\ Gm\approx9.46\times 10^{6}\ Gm$.

Step4: Convert to femtometers

We know that $1\ m = 10^{15}\ fm$. So, $d_{fm}=9.4607304725808\times 10^{15}\times10^{15}\ fm = 9.4607304725808\times 10^{30}\ fm\approx9.46\times 10^{30}\ fm$.

Answer:

a) $9.46\times 10^{24}\ nm$
b) $9.46\times 10^{6}\ Gm$
c) $9.46\times 10^{30}\ fm$