Question

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 ?

Short answer

Answer

$$\begin{gathered} \text{(a)}{\text{10}}^9\text{μmmakeup1.04km.} \\ \text{(b)}{\text{10}}^{-4}\text{fractionofacentimeteris1.0}\mathrm{\mu m} \\ \text{(c)}{\text{Thereare9,144×10}}^5\mathrm{\mu m}\text{in1.0yd.} \end{gathered}$$

Step-by-step solution

Understanding the unit conversion 

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:

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

(a) Conversion of kilometers into microns 

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.

(b) Determination of fraction of centimeter

Using the conversion factor, calculate the fraction of centimeters.

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

(c) Conversion of yard into microns

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$9.144\times {10}^5\mu m$ .