# Question 79a10

Sep 27, 2015

$\approx 2.54 \cdot {10}^{5} \text{nm}$

#### Explanation:

You could probably estimate the diameter of grain of medium sand to be equal to $\frac{1}{100} \text{inch}$, according to the following sources

To convert this value to nanometers, you first need to convert it to centimeters by using the following conversion factor

$\text{1 inch" = "2.54 cm}$

You know that a meter is equal to ${10}^{9}$ nanometers, and equal to ${10}^{2}$ centimeters, which means that you can go from centimeters to nanometers by using the conversion factor

$\text{1 cm" = 10^7"nm}$

The diameter of the grain of sand will be

1/100color(red)(cancel(color(black)("in"))) * (2.54color(red)(cancel(color(black)("cm"))))/(1color(red)(cancel(color(black)("in")))) * (10^7"nm")/(1color(red)(cancel(color(black)("cm")))) = color(green)(2.54 * 10^5"nm")

Notice that this is exactly what you get when you use

1/100color(red)(cancel(color(black)("in"))) * (2.54color(red)(cancel(color(black)("cm"))))/(1color(red)(cancel(color(black)("in")))) * (1color(red)(cancel(color(black)("m"))))/(10^2color(red)(cancel(color(black)("cm")))) * (10^9"nm")/(1color(red)(cancel(color(black)("m")))) = color(green)(2.54 * 10^5"nm")#