Question

Question #79a10

Answer 1

`~~2.54 * 10^5"nm"`

Explanation:

You could probably estimate the diameter of grain of medium sand to be equal to `1/100"inch"`, according to the following sources

https://en.wikipedia.org/wiki/Grain_size
http://hypertextbook.com/facts/2000/IlanaPrice.shtml
http://hypertextbook.com/facts/2003/MarinaTheodoris.shtml

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

`"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

`"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")`