Question

measured in meters, the wavelength of red light is about 8 × 10^-7, and the wavelength of violet light is 4 × 10^-7. the wavelength of red light is how many times longer than the wavelength of violet light? 8 × 10^-7 m 4 × 10^-7 m 2 times as long 4 times as long 10^2 times as long 10^7 times as long

Explanation:

Step1: Set up division formula

To find out how many times the wavelength of red - light is longer than that of violet - light, we divide the wavelength of red light by the wavelength of violet light. The wavelength of red light is $8\times10^{-7}$ m and the wavelength of violet light is $4\times10^{-7}$ m. So the formula is $\frac{8\times 10^{-7}}{4\times 10^{-7}}$.

Step2: Use the rule of dividing numbers in scientific notation

According to the rule $\frac{a\times10^{n}}{b\times10^{m}}=\frac{a}{b}\times10^{n - m}$, here $a = 8$, $b = 4$, $n=-7$, $m = - 7$. Then $\frac{8\times 10^{-7}}{4\times 10^{-7}}=\frac{8}{4}\times10^{-7-(-7)}$.

Step3: Calculate the result

$\frac{8}{4}=2$ and $10^{-7-(-7)}=10^{0}=1$. So $\frac{8}{4}\times10^{-7 - (-7)}=2\times1 = 2$.

Answer:

2 times as long