Q3P - Fundamentals Of Physics

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 ?

Step-by-Step Solution

Answer

Answer

 $$\begin{gathered} \text{ (a)}{\text{ 10}}^9\text{μm make up 1.04 km .} \\ \text{ (b)}{\text{ 10}}^{-4}\text{ fraction of a centimeter is 1.0 }\mathrm{\mu m} \\ \text{ (c)}{\text{There are 9,144×10}}^5\mathrm{\mu m}\text{ in 1.0 yd .} \end{gathered}$$

Step 1: 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: 

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

Step 2: (a) Conversion of kilometers into microns

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

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

Thus,${ 10}^9\mu m$   make up 1.0 km.

Step 3: (b) Determination of fraction of centimeter

Using the conversion factor, calculate the fraction of centimeters.

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

Step 4: (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.

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

  

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