Unit Converting

The factor labeling method

How to Convert Units

Lets start with a question and then go through the steps.

How many seconds are there in a year?

Step 1:

Write the value you want to convert along with the units.

1 year

Step 2

Draw a set of parentheses with a fraction bar inside next to the value you have just written. We will use this every time we try to convert.

1 year ( )

Step 3

1 year ( )

Choose and write a conversion equality.

What can we convert years into?

1 year = 365 days

Step 4

Next is to place our units (AND JUST UNITS) into the fraction.

Before we do that, we need to recognize the 2 different parts of a fraction, and we need to recognize that the units for a value are also included in these 2 different parts.

X

Y

Numerator (Top)

Denominator (Bottom)

Also applies to units:

m

s

Step 4 Continued

For a number like:

70 meters

What part of a fraction are the units for this number in (numerator or denominator)?

70 meters = 70 meters

1So, meters are in the numerator.

Step 4 ContinuedNext is to place our units (AND JUST UNITS) into the fraction.

1 year ( )

1 year = 365 days

In order to cancel out Years, do we put years in the denominator or the numerator of the fraction?

It should go in the denominator!

year

Step 5The units you are converting into should be placed on the other side of the fraction.

1 year ( )

1 year = 365 days

year

days

Step 6WARNING!!!! No thinking required!

We need to place our numbers into the fraction. To do this put the number that comes before the unit in the conversion equality before that unit again in your fraction.

1 year ( )

1 year = 365 days

year

days

1

365

Step 7

Now just solve!

-Multiply all the numerators together

-Multiply all the denominators together

-Cross out any units that are both on the top and the bottom

-Write your answer with your new units

1 year ( )year

days

1

365= days365

Going Forward

1 year ( )year

days

1

365= days365

Repeat the steps until you are converted into the units you want.

days365 ( )days

hours

1

24

1 day = 24 hours

= 8760 hours

. . . 31,536,000 seconds

Slightly Harder

Convert 15 km/hour into m/sec

15 kmhour

Do one unit at a time.

Lets say you would like to do hours into seconds first, just keep in mind that hours is in the denominator now, so where do you need to put hours in your fraction?

The Numerator!

( )hour

min

1 hour = 60 min

60

1…

Conversion Steps

1. Write the value you want to convert along with the units.

2. Draw a set of parentheses with a fraction bar inside next to the value you have just written. 3. Choose and write a conversion equality.

4. Place our units (AND JUST UNITS) into the fraction.

5. The units you are converting into should be placed on the other side of the fraction.

6. Place our numbers into the fraction.

7. Solve.