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We use different units to measure different quantities like length, weight, and time. And we have multiple units to choose from for a single quantity. The units that we commonly use to measure quantities belong to two systems of units: the metric system and the customary system. We will learn how to convert a quantity measured in one unit into another unit....Read MoreRead Less

The metric system uses the meter, liter, and gram as base units of length (distance), capacity (volume), and weight (mass), respectively. In the metric system, the powers of ten can be used to find equivalent measures.

It’s also known as the U.S. Customary System. Customary units are used mainly in the United States. Units such as feet, gallons, pounds and so on are part of the **Customary System**.

Let’s consider an example to understand the methods of conversion measures within the same system.

Converting 32 quarts to gallons.

As we know that 4 quarts = 1 gallon, which means that there are \(\frac{1}{4}\) gallons per quart.

**Method 1:**

Using the unit rate of 4 quarts per gallon to create a ratio table. To calculate the number of gallons in 32 quarts, we have to multiply each quantity by 8.

As a result, 32 quarts equals 8 gallons.

**Method 2:**

Making a ratio table with \(\frac{1}{4}\) gallon per quart as the unit rate. To find the number of gallons in 32 quarts, we have to multiply each quantity by 32.

As a result, 32 quarts equals 8 gallons.

**Method 3:**

A graph can be used to convert one quantity to another.

Take a graph sheet and the vertical axis indicates the gallons, and the horizontal axis indicates the quarts.

Plot the point (4, 1) on the graph sheet because 4 quarts = 1 gallon, similarly, plot (8,2) because 8 quarts = 2 gallons. Draw the line from the origin through these points and extend until it reaches 32 on the horizontal axis.

Now check the corresponding vertical axis value to find 32 quarts in gallons.

As a result, 32 quarts equals 8 gallons.

Let’s consider an example to understand the two methods of converting measures between systems.

Converting 8 miles to kilometers.

As we know that 1 mile = 1.6 kilometers (rounding to the nearest tenths). It means that \(\frac{1}{1.6}\) miles makes a kilometer.

**Method 1:**

Using the unit rate of 1.6 kilometers per mile to create a ratio table. To calculate the number of kilometers in 8 miles, we have to multiply each quantity by 8.

As a result, 8 miles equals 12.8 kilometers.

**Method 2:**

Making a ratio table with \(\frac{1}{1.6}\) miles per kilometer as the unit rate. To find the number of kilometers in 8 miles, we have to multiply each quantity by 8.

As a result, 8 miles is about \(\frac{8}{0.625}\) = 12.8 kilometers.

A conversion factor is a number that is multiplied or divided to convert one set of units into another. The appropriate conversion factor must be used when converting from one value to another.

To convert inches to feet, for example, the appropriate conversion value is 12 inches making up 1 foot. Hence, the conversion factors are 1 foot per 12 inches or 12 inches per 1 foot.

**For example,** Converting 22 quarts to liters.

As we know 1 quart (qt) = 0.95 liters.

22 quarts = \(22~(qt)\times \frac{0.95~liters}{1~qt}\)

22 quarts = 20.9 liters.

For example, if we convert 5 pounds to kilograms.

As we know, 1 pound (lb) = 0.45 kilograms (kg) (rounding to the nearest hundredths)

Using a double number line,

We have to draw two number lines parallel to each other as the name itself indicates a double number line. The first number line denotes the units in pounds and the second number line denotes the units in kilograms, each unit in the second number line has an increment of 0.45 kilograms from the immediate left.

We then plot 5 on the first number line, the corresponding value on the second number line gives the result.

As a result, 5 pounds = 2.25 kilograms.

**Example 1:** John needs to set up a fence around a 39 feet long vegetable garden. How much fencing does he require in meters?

**Solution: **As we know that 0.3 meters = 1 foot, and this means that 1 foot consists of 0.3 meters, and \(\frac{1}{0.3}\) foot per meter.

Using the unit rate of 0.3 meters per foot to create a ratio table.

As a result, 39 feet equals 11.7 meters.

**Example 2: **Ron drank 7 quarts of juice. What is the quantity of orange juice that Ron has consumed? Round the answer to the nearest hundredths, if necessary.

**Solution: **As we know that 1.057 quarts = 1 liter, this only indicates that \(\frac{1}{1.057}\) of a liter per quart. We then find an equivalent rate with 7 quarts using unit rates and ratio tables.

Create a ratio table with \(\frac{1}{1.057}\) liter per quart as the unit rate. To find the number of liters in 7 quarts, we have to multiply each quantity by 7.

As a result, 7 quarts equals to 6.6225 liters. Rounding to the nearest hundredth gives us 6.63 liters as the result.

**Example 3: **Joey brought a phone that measured 9 inches in length. How many centimeters does the phone measure? Use a conversion graph.

**Solution: **A conversion graph can be used to convert one quantity to another.

Take a graph sheet and the vertical axis indicates the centimeters and the values are the multiples of 2.54 because 1 inch is equal to 2.54 centimeters. And the horizontal axis indicates the inches.

Now we have to convert 9 inches to centimeters. Plot the point (1, 2.54) similarly, plot (2,5.08) because 2 inches is 5.08 cm and draw the line from the origin to these points.

Now extend the line until it reaches 9 on the horizontal axis.

Now check the corresponding centimeters towards the vertical axis to find 9 inches in centimeters.

As a result, 9 inches equals 22.86 centimeters.

**Example 4: **Rachel traveled 50 kilometers per hour in a car. How many miles did Rachel travel per minute ?

**Solution: **Converting 50 kilometers per hour to miles per minute.

As we know, 1 kilometer (km) is 0.621 miles (rounding to the nearest thousandths)

1 hour = 60 minutes

\( 50~\text{kilometers per hour} =\frac{50~(\text{kilometer})}{1~(\text{hour})}\times \frac{0.621~\text{miles}}{1~\text{kilometer}}\times \frac{1~(\text{hour})}{60~(\text{minutes})}\)

Therefore, 50 kilometers per hour is 0.5175 miles per minute.

As a result 50 kilometers per hour is about 0.5175 miles per minute. Rounding to the nearest hundredths gives us 0.52 miles per minute. Hence, Rachel traveled 0.52 miles per minute.

Frequently Asked Questions

The fact that any number or expression can be multiplied by “one” without changing its value is used in this process. The value of the conversion factor is 1. Hence, by multiplying or dividing by a conversion factor, the value of the quantity does not change, the quantity is only expressed in another way.

Rounding a measurement results in a less accurate measurement and introduces a certain quantity of error. When dealing with rounded measurements, we have to keep in mind the following aspects:

- Look at the value immediately to the right of the position that has to be rounded.

- If the value is 5 or greater, the place value should be rounded up by 1. Otherwise, we don’t change the place value.

**For example,** Rounding to the nearest tenths, 11.35 becomes 11.4. Rounding to the nearest tenths, 7.339 becomes 7.3.