### Video Transcript

A human hair has a diameter of
80000 nanometers. How many nanoparticles with a
diameter of 50 nanometers would fit across the human hair? Give your answer to the nearest
whole number.

Human hair varies in thickness by
quite a lot, but it’s typically 100 micrometers wide, which is about 100000
nanometers. The particular hair we’ve been
given is 80000 nanometers in diameter, which is just a little bit thinner. Nanoparticles are particles with a
diameter of 1 to 100 nanometers. The nanoparticles we’ll be using
have a diameter of 50 nanometers. I’ve assumed, in this case, we’re
dealing with spherical nanoparticles.

Our job is to work out how many of
these nanoparticles placed end to end would fit across the human hair. This means we need to work out how
many particles in a line are 80000 nanometers long. And we shouldn’t overthink it and
place the nanoparticles on the surface of the hair. To figure out the number of
nanoparticles we need, we simply have to take the diameter of the hair and divide it
by the diameter of the nanoparticle.

We plug in our values to get 80000
nanometers divided by 50 nanometers. We don’t necessarily need a
calculator for this because we can see that 50 goes into 800 16 times, which means
50 goes into 80000 1600 times, giving us our answer of 1600 nanoparticles. And we already have our answer to
the nearest whole number.