Question

a human hair is 75.0 μm across. how many inches is this? 75.0 μm × (10^(- 6) m / 1 μm) × (100 cm / 1 m) × (( ) / ( )) = 0.00295 in

Explanation:

Step1: Recall conversion factors

We know that \(1\ \mu m = 10^{- 6}\ m\), \(1\ m=100\ cm\), and \(1\ in = 2.54\ cm\).

Step2: Set - up the conversion

We start with \(75.0\ \mu m\). First, convert \(\mu m\) to \(m\): \(75.0\ \mu m\times\frac{10^{-6}\ m}{1\ \mu m}\). Then convert \(m\) to \(cm\): \(75.0\times10^{-6}\ m\times\frac{100\ cm}{1\ m}\). To convert \(cm\) to \(in\), we need to multiply by \(\frac{1\ in}{2.54\ cm}\).

Answer:

The missing part in the conversion is \(\frac{1\ in}{2.54\ cm}\)