Question

Suppose your hair grows at the rate of 1 25 inch per day. Find the rate at which it grows in nanometers per second.

Answer 1

We just need to convert, separately, inches to (nano)meters, and days to second.

One inch is 0.0254 meters, and there are 10^9 nanometers in one meter. So, there are $0.0254 \times 10^9$ nanometers in an inch.

On the other hand, one days is composed by 24 hours, each composed by 60 minutes each composed by 60 seconds. So, there are

$24 \times 60 \times 60 = 86400$ seconds in a day.

Now we can perform the substitution:

$1.25 \dfrac{\text{inch}}{\text{day}} = 1.25\times \dfrac{0.0254 \times 10^9\text{nanometer}}{86400\text{ seconds}} = \dfrac{1.25\times0.0254 \times 10^9\text{nanometer}}{86400\text{ seconds}}$

You can simplify the numeric part, getting

$1.25\times0.0254 \times 10^9 = 0.03175 \times 10^9 = 3.175 \times 10^7$

and thus

$\dfrac{3.175 \times 10^7}{86400} = 0.03674768518\times 10^7 = 3.674768518 \times 10^5$

So, that's the speed, misured in nanometers per second.