Sometimes multiple conversions are needed before we end up with the units we want. For example, How many minutes are there in two days? The process is the same, we just repeat the steps for every unit conversion we make.

**Steps for Unit Conversions**

- Look at the units you have.
- Figure out the units you want.
- Find the conversion factors that will help you step by step get to the units you want.
- Arrange conversion factors so that unwanted units cancel out.

The following video will show an example of using two conversion factors.

Video Source (04:34 mins) | Transcript

Time is one of the most commonly used conversions. Depending on what you are converting between, it is also a good example of sometimes needing more than one conversion factor.

Example:

How many minutes are there in two days?

Unless you know the conversion for minutes to days, this takes two conversion factors.

We can use the following equivalence statements to make our conversion factors.

1 day = 24 hours

1 hour = 60 minutes

First, we start with what we have which is two days.

Next, we use one of our equivalence statements to make the conversion factor that will allow us to cancel out “days.”

\(\displaystyle 2\text{ days} \times \frac{24\text{ hours}}{1\text{day}}\)

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

\(\displaystyle 2\cancel{{\color{Red} \text{ days}}} \times \frac{24\text{ hours}}{1\cancel{{\color{Red} \text{day}}}} \)

This leaves us with “hours” in the numerator. We still need another conversion factor to cancel out the “hours.” The conversion factor \(\frac{60\text{ minutes}}{1\text{ hour}}\) allows us to cancel out “hours” in the numerator with “hours” in the denominator.

\(\displaystyle 2\cancel{{\color{Red} \text{ days}}} \times \frac{24\cancel{{\color{Blue} \text{ hours}}}}{1\cancel{{\color{Red} \text{day}}}} \times \frac{60\text{ minutes}}{1\cancel{{\color{Blue} \text{ hour}}}} \)

This now leaves us with just “minutes” as our only units left.

Now that we have arrived at the units we want, we do the calculation.

\(\displaystyle \frac{2\times24\times60 \text{ minutes}}{1}= 2880 \text{ minutes} \)

Thus, two days = 2880 minutes.

Even though it took two conversion factors, we were still able to get to the answer.

The following video shows another example of multiple unit conversions, focusing on following the 4 step process.

Video Source (06:39 mins) | Transcript

**Steps for Unit Conversions**

- Look at the units you have
- Figure out the units you want
- Find the conversion factors that will help you step by step get to the units you want
- Arrange conversion factors so unwanted units cancel out

These are the general steps for doing unit conversions. Let’s use them in an example to demonstrate how it works.

Example: How many days is 5000 minutes?

Step 1: Look at the units you have.

We have 5000 minutes; the units we currently have are minutes.

Step 2: Figure out the units you want.

Our question wants us to find out how many days this is equivalent to. Days are the units we want to get to.

Step 3: Find the conversion factors that will help you step by step get to the units you want.

60 minutes = 1 hour

24 hours = 1 day

We use these equivalence statements to create our conversion factors to help us cancel out the unwanted units.

Step 4: Arrange the conversion factors so unwanted units cancel out.

\(\displaystyle \left ( 5000{\cancel{\color{Magenta} \text{ minutes}}} \right ) \left ( \frac{1\cancel{{\color{DarkOrange} \text{ hour}}}}{60\cancel{{\color{Magenta} \text{ minutes}}}} \right ) \frac{1\text{ day}}{24\cancel{{\color{DarkOrange} \text{ hours}}}} \)

The next key to getting the correct answer is to do the calculations correctly. This is a place where students sometimes make mistakes.

There are two ways to go about doing this calculation.

**Multiply Numerators and Denominators and then divide.**

The first method is to multiply everything in the numerator together, and multiply everything in the denominator together.

Then divide.

(This is demonstrated in the video: Unit Conversions for Time (4:34 mins; Transcript))

\(\displaystyle \frac{\text{Everything in numerator}}{\text{Everything in denominator}}=\frac{5000\times1\times1\:\text{day}}{60\times24}=\frac{5000}{1440}= 3.47222\text{...days} \)

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

**Zig-Zag Method**

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.

Any time you go down to the denominator you divide.

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

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

\(5000\div 1 \times 1\div 60\times 1 \div 24 = 3.47222\text{...}\)

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

## Additional Resources

- Khan Academy: Converting Units: Minutes to Hours (4:53 mins | Transcript)
- Khan Academy: Multi-Step Unit Conversion Examples (5:37 mins | Transcript)

### Practice Problems

1 day = 24 hours

(

1 hour = 60 minutes

1 minutes = 60 seconds

(

1 week = 7 days

1 hour = 60 minutes

(

1 minute = 60 seconds

1 hour = 60 minutes

(

1 minutes = 60 seconds

(

1 week = 7 days

1 day = 24 hours

(

60 minutes = 1 hour

(

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