Question #79a10

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")#