Question

the speed of light is about 300,000,000 meters per second. that’s about 3×10^8 meters per second. the speed of sound in dry air is about 3×10^2 meters per second. about how many times faster does light travel than sound in dry air? speed of sound in dry air speed of light 3×10^2 m/s × 10^? = 3×10^8 m/s

Explanation:

Step1: Set up division formula

To find out how many times faster light travels than sound, we divide the speed of light by the speed of sound. The speed of light is $3\times10^{8}$ m/s and the speed of sound is $3\times10^{2}$ m/s. So the formula is $\frac{3\times 10^{8}}{3\times 10^{2}}$.

Step2: Use exponent - division rule

According to the rule $\frac{a\times10^{m}}{a\times10^{n}}=10^{m - n}$ (where $a = 3$, $m = 8$, $n = 2$), we have $\frac{3}{3}\times10^{8 - 2}$.

Step3: Simplify the expression

$\frac{3}{3}=1$, and $8-2 = 6$. So the result is $1\times10^{6}=10^{6}$.

Answer:

$10^{6}$