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.
Note: your answer should be in the form of one or more fractions multiplied together.

Answer 1

`(1,000 g)/(1 kg)` ·
`(100 cm)/(1 m)`

Step-by-step explanation:

The final answer has a different set of units. In particular, kilograms (kg) changes to grams (g) and meters (m) changes to centimeters (cm). To make this change, you need to multiply the first value by proportions.

When writing these proportions, it is important that they are arranged in a way that allows for the cancellation of units. For instance, since both kg and m are located in the numerator, they must be located in the denominators of the conversions.

Proportions:

1 kg = 1,000 g

1 m = 100 cm

The full expression:

`-4.3*10^4 (kg*m)/(s)` ·
`(1,000 g)/(1 kg)` ·
`(100 cm)/(1 m)` =
`?(g*cm)/(s)`

^ ^

As you can see, the old units cancel out and you are left with g and cm in the numerator.