Introduction

Steps for Unit Conversions

1. Identify the units you have.
2. Identify the units you want.
3. Find the conversion factors that will help you step-by-step get to the units you want.
4. Arrange conversion factors so that unwanted units cancel out through cross-cancellation.

These videos illustrate the lesson material below. Watching the videos is optional.

• Unit Conversion for Time (04:34 mins) | Transcript
• Steps for Unit Conversion (06:39 mins) | Transcript

Unit Conversions for Time

Time is one of the most commonly used conversions. Sometimes, it can also be a good example of needing more than one conversion factor.

Example 1
How many minutes are in two days?

Unless you know the conversion for minutes to days, this takes two conversion factors. You can use the following equivalence statements to make the conversion factors.

• $1day=24hours$
• $1hour=60minutes$

First, start with known information, which is 2 days. Next, use one of the equivalence statements to make the conversion factor that will allow you to cancel out “days.”

Hint: Look for the equivalence statement that has "days" in it. Then, write the conversion factor so cross-cancellation can be used to cancel "days".

$$\begin{array}{r}2\text{ days}\times \frac{24\text{ hours}}{1\text{ day}}\end{array}$$

The conversion factor $\frac{24\text{hours}}{1\text{day}}$ allows you to cancel “days” in the numerator with “days” in the denominator.

$$\begin{array}{r}2\cancel{\text{ days}}\times \frac{24\text{ hours}}{1\cancel{\text{day}}}\end{array}$$

This leaves you with “hours” in the numerator. Because the problem asked for minutes, you still need another conversion factor to cancel out the “hours.” The conversion factor $\frac{60\text{ minutes}}{1\text{ hour}}$ allows you to cancel out “hours” in the numerator with “hours” in the denominator.

$$\begin{array}{r}2\cancel{\text{ days}}\times \frac{24\cancel{\text{ hours}}}{1\cancel{\text{day}}}\times \frac{60\text{ minutes}}{1\cancel{\text{ hour}}}\end{array}$$

This leaves you with just “minutes” as the only units left. Now that you have arrived at the units you want, do the calculation.

$$\begin{array}{r}\frac{2\times 24\times 60\text{ minutes}}{1\times 1}=2880\text{ minutes}\end{array}$$

Thus, $2days=2880minutes$.

Example 2
How many days is 5000 minutes?

Here are the equivalence statements that will help you get to the units you want.
$$\begin{array}{r}60minutes=1hour\\ \\ 24hours=1day\end{array}$$

Use these equivalence statements to create conversion factors in a way that unwanted units will cancel out. Then, add the known information and multiply it by the conversion factors:
$$\text{Missing begin{align*} or extra end{align*}}$$

Be sure to do the calculations correctly. This is a place where students sometimes make mistakes. There are two methods to calculate:

• Method 1: Multiply Numerators and Denominators and then Divide
• Method 2: Zig-Zag Method

The first method is to multiply everything in the numerator together, and multiply everything in the denominator together, and then divide.
$$\begin{array}{r}\frac{\text{Everything in numerator}}{\text{Everything in denominator}}=\frac{5000\times 1\times 1\text{day}}{60\times 24}=\frac{5000}{1440}=3.47222\text{...days}\end{array}$$

So $5000minutes=3.5days$ (rounded to nearest tenth).

The other method to properly calculate several fractions being multiplied together is to use the zig-zag method. The zig-zag method says to calculate the numbers going in a zig-zag pattern starting with the first numerator.

Figure 1

Any time you go down to the denominator you divide.

Figure 2

Any time you go up to the next numerator you multiply.

Figure 3

This method makes putting the numbers into your calculator very quick. In this case, enter the following into your calculator going from left to right:

$$\begin{array}{r}5000÷1\times 1÷60\times 1÷24=3.47222\text{...}\end{array}$$

If you round to the nearest tenth, this means $5000min=3.5days$.

Things to Remember

• There must be a unit in the denominator and the same unit in the numerator of the next fraction for the units to cancel out.
• When calculating, use one of the following methods:
  
  • Multiply the numerator. Multiply the denominator. Divide.
  • Use the zig-zag method: Divide numerator and denominator. Multiply when going up from the denominator to the numerator of the next fraction.

Practice Problems