Question: The micrometer $\left(1\mu m\right)$ is often called the micron. (a) How many microns make up 1km ? (b) What fraction of a centimeter equals $\left(1\mu m\right)$? (c) How many microns are in 1.0 yd ?

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors.Here, it is the conversion of length from one unit to another.

Conversion factors are given as follows:

$$\begin{gathered} {\text{1m=10}}^6\text{μm} \\ {\text{1km=10}}^3\text{m} \\ {\text{1cm=10}}^4\text{μm} \\ \text{1yard=3feets} \\ \text{1ft=0.3048m} \end{gathered}$$

Using the above conversion factors, convert km to the micron,

$$\begin{gathered} {\text{1km=10}}^3\text{m×}\frac{{10}^6\mu m}{1m} \\ {\text{=10}}^9\mu m \end{gathered}$$

Thus,${10}^9\mu m$ make up 1.0 km.

Using the conversion factor, calculate the fraction of centimeters.

$$\begin{gathered} 1\mu m=\frac{1}{{10}^{6}m} \\ 1\mu m=\frac{1}{{10}^{6}m}\times \left(\frac{100cm}{1m}\right) \\ \frac{1\mu m}{1cm}={10}^{-4} \\ \text{Thus,}{10}^{-4}\text{fractionofacentimeteris}1.0\mu m\text{.} \end{gathered}$$

Using the conversion factors for yards to feet, feet to meters and meters to micron, convert yards to microns.

$$\begin{gathered} 1.0yd=3ft\times \left(\frac{0.3048m}{1ft}\right)\times \left(\frac{{10}^6\mu m}{1m}\right) \\ =9.144\times {10}^5\mu m \end{gathered}$$

Thus, 1 yd in there are$9.144\times {10}^5\mu m$ .