### Key Concepts

• Convert from metric units to customary units.

• Convert from customary units to metric units.

• Convert using two steps.

**5.9 Relate customary and metric units**

Recall that there are two primary systems of measurements:

**The customary system:** This system of measurement is primarily used in the United States, which include the inch, foot, mile, pound and cup.

**The metric system: **This system of measurement is primarily used in science and in countries outside the United States, which include meter, kilometer, liter, gram and kilogram.

- Anytime you are converting a smaller unit of measure to a larger unit of measure, we need to divide by a conversion factor.
- Anytime you are converting a larger unit of measure to a smaller unit of measure, we need to multiply by a conversion factor.

**Example 1: **Ann is on a road trip with her family. He sees a sign on the board saying the limit is 40 km per hour. Help Ann understand the sign as she is from United States, who is not familiar with the metric system.

**Solution: **First, Ann should see how are kilometers and miles related. She should notice that 1 mile is approximately equal to 1.61 kilometers.

Now, because she is going from metric(smaller unit) to customary(bigger unit), she will need to divide the given value by the metric equivalent. Keeping in mind that 1.61 is approximately 1.6.

### Customary and metric equivalents of length:

### Customary and metric equivalents of Capacity:

### Customary and metric equivalents of Weight/mass:

**5.10.1 Convert from metric units of customary units**

**Example 1:**

Rebecca is constructing a wall of height 4 meters. What will be its height in inches?

**Method: 1 (Using equivalent rate)**

**Solution:** Find an equivalent rate to convert meters into inches.

**Step 1: **Find a relation between meters and inches. Notice that 1 meter is approximately equal to 39.37 inches.

**Step 2: **Write the equivalent rate in fraction. Multiply both the terms of the rate by 4.

39.37 inches / 1 meter =39.37 × 4 / 1 × 4=157.48 inches / 4 meters

**Step 3: **Round to the nearest tenth of an inch.

157.48 ≈ 157.5

So, 4 meters ≈ 157.5 inches.

**Method: 2 (Using conversion factor)**

**Conversion factor: **A conversion factor is a rate that compares equivalent measures.

**Step 1:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

4 m × 39.37 inches / 1 m

**Step 2:** Divide out the common units.

4 × 39.37 inches= 157.48 inches.** **

**Step 3: **Round to the nearest tenth of an inch.

157.48 ≈ 157.5

So, 4 meters ≈ 157.5 inches.

**Example 2: **Jose plans to move from Vancouver to Hope, which is a 150 km journey. Help Jose in understanding the distance in miles, as he is from Boston.

**Method: 1**

**Solution:**

**Step 1: **Find a relation between kilometers and miles. Notice that 1 kilometer is approximately equal to 1.61 km.

**Step 2: **Divide the given kilometers by its equivalent customary unit.

150 ÷ 1.61 = 93.16

**Step 3: **Round to the nearest tenth of a mile.

93.16 ≈ 93.2

So, 150 kilometers ≈ 93.2 miles.

**Method: 2 (Using conversion factor)**

**Step 1:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

150 km × 1 mile / 1.61 km

**Step 2:** Divide out the common units.

150 miles ÷ 1.61 = 93.16 miles.

**Step 3: **Round to the nearest tenth of a mile.

93.16 ≈ 93.2

So, 150 kilometers ≈ 93.2 miles.

**5.10.2 Convert customary units to metric units **

**Example 1: **A zoo has a tiger and a cat weighing 420 pounds and 15 pounds, respectively. What is the combined weight of both the animals in kilograms?

**Method: 1**

**Solution:** Add weights of both the animals in pounds.

Weight of tiger + Weight of cat = 420+15 = 435 pounds.

**Step 1: **Find a relation between kilograms and pounds. Notice that 1 kilogram is approximately equal to 2.20 lb.

**Step 2: **Divide the given pounds by its equivalent metric unit.

435 ÷ 2.20 = 197.72 kilograms.

**Step 3: **Round to the nearest tenth of a kilogram.

197.72 ≈ 197.7

So, 435 pounds ≈ 197.7 kilograms.

**Method: 2 (Using conversion factor)**

**Step 1:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

435 pounds × 1 kg / 2.20 pounds

**Step 2:** Divide out the common units.

435 kg ÷ 2.20 = 197.72 kgs.

**Step 3: **Round to the nearest tenth of a kilogram.

197.72 ≈ 197.8

So, 435 pounds ≈ 197.7 kilograms.

**Example 2: **A container brought 2200 pounds of rice grains. The rice grains must be packed into bags each weighing 50 kg. How many bags of rice can be obtained?

**Method: 1**

**Solution:**

**Step 1: **Find a relation between kilograms and pounds. Notice that 1 kilogram is approximately equal to 2.20 lb.

**Step 2: **Divide the given pounds by its equivalent metric unit.

2200 ÷ 2.20 = 1000 kilograms.

**Step 3: **Divide the total weight in grams by 50, to obtain the number of bags.

1000 ÷ 50 = 20 bags.

Therefore, 20 bags of rice each weighing 50 kg can be obtained.

**Method: 2 (Using conversion factor)**

**Step 1:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

2200 pounds × 1 kg / 2.20 pounds

**Step 2:** Divide out the common units.

2200 kg ÷ 2.20 = 1000 kgs.

**Step 3: **Divide the total weight in grams by 50, to obtain the number of bags.

1000 ÷ 50 = 20 bags.

Therefore, 20 bags of rice each weighing 50 kg can be obtained.

**5.10.3 Convert using two steps**

**Example 1: **Chris brings 18 liters of grape juice for the party. How many cups can be made to serve the guests?

**Solution:** Convert liters to quarts, and then quarts to cups. Find a relation between liters and quarts. Notice that 1 liter is approximately equal to 1.06 quart.

**Step 1:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

18 L × 1.06 quart / 1 L

Divide out the common units.

18 × 1.06 quarts = 19.08 quarts

Round to the nearest tenth of a quart.

19.08 ≈ 19.1

So, 18 liters ≈ 19.1 quarts.

Convert quarts to cups, find a relation between quarts and cups. Notice that 1 quart is equal to 4 cups.

**Step 2:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

19.1 quarts ×

4 cup1 quart4 cup1 quart

Divide out the common units.

19.1 × 4 cups = 76.4 cups.

**Example 2: **What is the length of 100-yards football field in meters?

**Method: 1**

**Solution:** Convert yards to feets, and then feets to meters. Find a relation between yards and feets. Notice that 1 yard is equal to 3 feet.

**Step 1:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

100 yards × 3 feet / 1 yard

Divide out the common units.

100 × 3 feet = 300 feet.

Convert feets to meters, find a relation between feet and meters. Notice that 1 meter is approximately equal to 3.28 feet.

**Step 2:** Multiply by the conversion factor that relates the measures and leaves you with the units needed to solve the problem.

300 feet ×

1 meter3.28 feet1 meter3.28 feet

Divide out the common units.

300 meters ÷ 3.28 = 91.46 meters.

Step 3: Round to the nearest tenth of a meter.

91.46 ≈ 91.5

Therefore, a football field of 100 yards ≈ 91.5 meters.

## Exercise:

1. Martin is building a mannequin 80 inches tall, to the nearest tenth; how many meters tall is the mannequin?

2. If the perimeter of the baseball ground is 2 km, what is the perimeter in miles?

3. Deva’s weight is 250 pounds in the month of January. If he loses 80 pounds in three months. What is his current weight in kilograms?

4. Jacob bought 40 pints of white paint to color his apartment Estimate the quantity of paint in liters.

5. A chef at a restaurant uses 15 pounds of cheese per day. About how many grams of cheese is used in day?

6. A person must be 145-centimeters-tall to climb a giant wheel. If Abdul is 4 feet 5 inches, does he qualify to climb the giant wheel?

7. The weight of car is 1.5 ton. What would the weight be in terms of pounds?

8. Convert 10 liters of water to cups.

9. If the length of the door is 13 feet. What is its length in meters?

10. If the weight of a rabbit 16 oz. What is the weight 10 rabbits in kilograms?

### What have we learned?

■ Converting from metric units to customary units.

■ Converting from customary units to metric units.

■ Converting using two steps.

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