Wavelengths in nm to frequency

[Noctix]

Homework Statement

The human eye is sensitive to light of wavelengths from about 400 to 700nm. What range of frequencies does this range correspond to? Take the speed of light to be 3.00 x 10^8 m/s.

Homework Equations

f=v/lambda

The Attempt at a Solution

3.00 x 10^8 / 400,000m = 750 HZ

I didn't bother to find the frequency for 700nm because i know 750hz is wrong... the answer for frequency of 400nm is supposed to be 4.3x10¹⁴, but i have no idea why.
thanks for the help!

 

[jambaugh]

400nm is not 40,000m.
Nanometers are small. To remember the powers of 10 remember the rhyme:

"mili-micro-nano-pico"
Each is a factor of 1/1000 so 400nm = 400/(1000,000,000) meters or 4x10^ -7 m.

now v/lambda = 3/4 10^8/10^-7 = .75 x 10^(8+7) = .75 x 10^15 = 7.5 x 10^14.
Or 750,000,000,000,000 equals (let's see kilo-mega-giga-tera) 750TeraHz.