**Using conversion factors to solve problems :**

We solve many real word problems by converting units within measurement system (metric or customary) and between measurement systems (customary to metric or metric to customary).

We use conversion factors to convert units within measurement system and between measurement systems.

The chart given below can be used to convert units within measurement system.

The chart given below can be used to convert units between measurement systems.

For example,

From the above chart, in the length section of customary to metric conversion, we have

1 inch = 2.54 centimeters

If we convert inches into cm, the conversion factor is

2.54 cm / 1 inch

If we convert cm into inches, the conversion factor is

1 inch / 2.54

**Example 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.

Hence, Elena needs 8 quarts of milk.

**Example 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.

**Example 3 :**

While working out, Alima adds 11.35 kilograms to the machine. About how many pounds does she add ?

**Solution :**

**Step 1 :**

Find the conversion factor for converting kilograms to pounds

1 kilogram **≃ ** 2.20 pounds

Write the conversion factor as a ratio

2.20 pounds / 1 kilogram

**Step 2 :**

Convert the given measurement.

Hence, Alima adds about 25 pounds.

**Example 4 :**

Bob’s driveway is 45 feet long by 18 feet wide. He plans to pave the entire driveway. The asphalt paving costs $24 per square meter. What will be the total cost of the paving ?

**Solution :**

**Step 1 :**

First find the dimensions of the driveway in meters.

Convert each measurement to meters.

Use 1 foot **≃** 0.305 meter.

**Step 2 :**

Next find the area in square meters.

Area = length × width

**≃ ** 13.725 × 5.49

**≃** 75.35025 square meters

**Step 3 :**

Now find the total cost of the paving.

square meters × cost per square meter = total cost

75.35025 × $24 **≃** $1,808.41

Hence, the total cost of the paving is $1808.41

After having gone through the stuff given above, we hope that the students would have understood "Using conversion factors to solve problems".

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