How many 10nm cubes fit into a 1 cm cube?

Answer 1

Conversion Factors:

• 1 meter (m) = 109 nanometers (nm)
• 1 m = 102 centimeters (cm)

Conversion Factors can be written as a fraction, with one side of the formula in the numerator (top) and one side in the denominator (bottom).

Example: ( 1 m / 109nm ) or ( 109nm / 1 m )

Combine the conversion factors in a way, so that meters cancel out, because we don't have meters in the initial problem. Units can cancel, just like any other factor using a fraction.

( 109nm / 1 m ) x ( 1 m = 102cm ) = 109nm / 102cm = 107 nm / cm

This translates to: 1 cm = 107 nm

Convert either unit into the other, using thederivedconversion factor we just came up with. I'm going to convert the 10 nm into cm's because it's easier.

10 nm x ( 1 cm / 107nm ) = 10 / 107 nm = 1 / 106 nm = 10-6 nm

Note: You can move a number raised to an exponent from the numerator to the denominator, or the other way, as long as the polarity of the power changes. Polarity is just negative or positive. This was an optional step, I did it because it just is easier than expressing a fraction.

Now Volume of a Cube, is going to be side cubed: V = s3

Volume of small cubes = (10-6cm)3 = 10-18cm3

Volume of the larger cube = (1 cm)3 = 1 cm3

To figure out how many cubes fit into the larger cubes, divide the volume of the larger cube by the volume of a single smaller cube. The units cancel out, which makes sense because this is a "counting number", that is, you really don't say I have 3 second apples, you just say I have 3 apples.

1 cm3/ 10-18cm3= 1018

Remember, you can move numbers raised to a power along the numerator and denominator as long as the polarity of the power changes.

The answer is 1018 cubes. That's a 1 with 18 zeros following it, orone quintillion.

Answer 2

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