CONVERTING UNITS BY USING CONVERSION FACTORS

We can convert the given customary unit to other unit by multiplying a conversion factor. A conversion factor is a ratio comparing two equivalent measurements.

Use the table below to find the conversion factor.

For example,

From the above table, in the length section of customary measurements, we have

1 foot  =  12 inches

If we convert feet into inches, the conversion factor is

12 inches/1 foot

If we convert inches into feet, the conversion factor is

1 foot/12 inches

Solved Problems

Problem 1 :

Elena wants to buy 2 gallons of milk but can only find quart containers for sale. How many quarts does she need ?

Solution :

Step 1 :

We want to convert gallons to quarts.

Identify the ratio that compares the units involved.

The units gallons and quarts are customary units of capacity.

Find the relationship of those units in the capacity section of the customary measurements table.

4 quarts  =  1 gallon

The appropriate conversion factor is 4/1.

Because when we multiply 2 gallons by that conversion factor, we can divide out the common unit gallons. The resulting unit is quarts.

Step 2 :

Multiply the given measurement by the conversion factor.

So, Elena needs 8 quarts of milk.

Problem 2 :

A container of a powdered fruit drink mix has a mass of 1.25 kilograms. What is that mass in milligrams ?

Solution :

Step 1 :

You want to convert kilograms to milligrams.

There is no equation in the table that relates kilograms and milligrams directly. However, we can convert kilograms to grams first. Then we can convert grams to milligrams.

Step 2 :

Multiply the given measurement by the conversion factor.

We can also do both conversions at the same time.

A mass of 1.25 kilograms is equal to 1,250,000 milligrams.

Problem 3 :

An oak tree is planted when it is 250 centimeters tall. What is the height of the oak tree in meters ?

Solution :

Step 1 :

We want to convert gallons to quarts.

Identify the ratio that compares the units involved.

The units centimeters and meters are metric units length.

Find the relationship of those units in the length section of the metric measurements table.

1 meter  =  100 centimeters

The appropriate conversion factor is 1/100.

Because when we multiply 250 centimeters by the conversion factor, we can divide out the common unit centimeters. The resulting unit is meters.

Step 2 :

Multiply the given measurement by the conversion factor.

So, the height of the oak tree is 2.5 meters.

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