A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation.

Question

A student sets up the following equation to convert a measurement. (The ? stands for a number the student is going to calculate.) Fill in the missing part of this equation.

(0.060 cm³)•__= ? m³

Answer 1

Hello, Kylia,

(0.060 cm³)•__= ? m³

We have units of cm³ and want units of m³. We know that 100 cm = 1 meter. We can wrtie that as:

100cm/1 meter

This is a conversion factor. It says 100 cm is equal to 1 meter. Since they are equal, this factor is equivalent to 1, with the only change coming in which unit is used. Since conversion factors are always equal to 1, they can be multiplied by anything, and although the number changes because of the unit change, it is still a vaild number. That includes multiplying (100cm/1 meter) by itself, which I'll do here:

(100cm/1 meter)³ = 1 x 10⁶ cm³/m³

A conversion factor may also be inverted (it is still equal to 1):

1/(1 x 10⁶ cm³/m³)

= (1x10^-6 m³/cm³)

We can use this new conversion factor to covert our volume from cm³ to m³.

(0.060 cm³)•(1x10^-6 m³/cm³ ) = ? m³

(0.060 cm³)•(1 x 10⁶ cm³/m³ ) = 6.0x10^-8 m³

Bob