**The Basic Concepts of Measurement**

Many times in real-life situations, you must convert measurement units from one form to another. For example, you may need to change feet to yards, or quarts to gallons, etc. There are several mathematical methods that can be used. The easiest one to use is to multiply or divide.

*To change from a larger unit to a smaller unit,* *multiply**by the conversion factor. To change from a smaller unit to a larger one,* *divide**by the conversion unit* .

The conversion units in the tables in this chapter are arranged in descending order: i.e., the largest unit is on top, and the smallest unit is at the bottom. This chapter includes conversion units for length, weight, capacity, and time. Only the most common units of measurement are explained in this section. Units such as rods, nautical miles, fathoms, and barrels have been omitted.

**Measures of Length**

Length is measured in inches, feet, yards, and miles ( Table 10.1 ).

**Examples**

**Example 1**

Change 5 yards to feet.

**Solution 1**

Since we are going from large to small, and the conversion factor is 1 yd = 3 ft, we multiply by 3 ft:

5 yd × 3 ft = 15 ft

**Example 2**

Change 648 inches to feet.

**Solution 2**

Since we are going from small to large, and the conversion factor is 1 ft = 12 in., we divide:

648 in. ÷ 12 in. = 54 ft.

Sometimes it is necessary to use an operation more than once to arrive at the solution.

**Example 3**

Change 79,200 feet to miles.

**Solution 3**

Since no conversion factor for changing feet to miles is given in Table 10.1 , it is necessary to convert feet to yards and then convert yards to miles:

**Math Note:** If you know the conversion factor 1 mile = 5280 feet, it is only necessary to divide once: 79,200 ft ÷ 5280 ft = 15 mi

**Mixed Units Conversions**

Another type of conversion has mixed units.

**Example 4**

Change 8 feet 7 inches to inches.

**Solution 4**

First change 8 feet to inches and then add 7 inches to the answer:

**Example 5**

Change 35 feet to yards and write the remainder in feet.

**Solution 5**

Hence, the answer is 11 yd 2 ft.

**Math Note:** The answer in the previous problem could also be written as yards.

**Example 6**

Change 8 yards 15 inches to yards.

**Solution 6**

**Measures of Length Practice Problems**

**Practice**

Change:

1. 16 ft to inches

2. 189 ft to yards

3. 9 ft 6 in. to inches

4. 19 yd to inches

5. 24,640 yd to miles

6. 14 mi to feet

7. 31,680 ft to miles

8. 6000 yd to miles (write the remainder in yards)

9. 43 ft 9 in. to feet

10. 19 yd 8 ft 5 in. to inches

**Answers**

1. 192 in.

2. 63 yd

3. 114 in.

4. 684 in.

5. 14 mi

6. 73,920 ft

7. 6 mi

8. 3 mi 720 yd

9.

10. 785 in.

Practice problems for these concepts can be found at: Measurement Practice Test.

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