**5.9 Convert Metric Units**

The metric units are a system of measurement, to move between different customary units of length, mass and capacity you will multiply or divide by a conversion factor.

- 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 divide by a conversion factor.

**Example 1: **Convert 289 centimeter to meter.

**Solution: **At first notice that centimeters are smaller than metre, which implies conversion of smaller unit to bigger unit has to be done.This means we need to divide. There are 100 centimeters in a meter, so the conversion factor becomes 100.

Now, take the given number of centimeters and divide by 100.

289 ÷ 100 = 2.89 meter.

**Example 2: **Convert 1.4 meter to centimeter.

**Solution: **At first notice that meter is bigger than centimeter, which implies conversion of bigger unit to smaller unit has to be done.This means we need to multiply. There are 100 centimeters in a meter, so the conversion factor becomes 100.

Now, take the given number of meters and multiply by 100.

1.4 × 100 = 140 cm.

The following charts provides an overview on metric units of length, capacity and mass.

**Metric units of length: **

**Metric units of capacity:**

**Metric units of mass:**

**5.9.1 Convert metric units of length**

**Example 1:**

Compare and decide which among 2.5 meter and 25.3 decimeter is greater.

**Method: 1**

**Solution:** To compare both the measurements must have same units. Here,let us convert and meter to decimeter to decide which one is greater.

At first notice that feet is meter is bigger than decimeter, which implies conversion of bigger unit to smaller unit has to be done.This means we need to multiply. There are 10 decimeters in a meter, so the conversion factor becomes 10.

Now, take the given number of meters and multiply by 10.

2.5 × 10 = 25 decimeter.

Therefore, among 25.3 decimeter is greater than 2.5 meter.

**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.

2.5 meter × 10 decimeter / 1 meter

Step 2: Divide out the common units.

2.5 × 10 decimeter = 25 decimeters.

Example 2: Susan joined a walking program, where she needs to walk 600 meters per day for five consecutive days in a week. Calculate the distance walked by her in week in terms of kilometers.

**Method: 1**

**Solution:** At first notice that kilometer is bigger than meter, which implies conversion of smaller unit to bigger unit has to be done.This means we need to divide. There are 1000 meters in a kilometer, so the conversion factor becomes 1000.

Distance walked per day = 600 meters.

Distance walked in 5 days = 600 x 5 = 3000m.

Now, take the given number of meters and divide by 1000.

3000 ÷ 1000 = 3 km

Therefore, Susan walks 3km in a week.

**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.

3000 meters × 1 kilometer / 1000 meters

Step 2: Divide out the common units.

3000km ÷ 1000 = 3 km.

**5.9.2 Convert metric units of capacity**

**Example 1: **Teresa poured 200 liters of water into a container. If the capacity of the container 2.8 hectoliters. How many more liters water is required to fill the container?

**Method: 1**

**Solution:** To compare, both the measurements must have same units. Here,let us convert hectoliters to liters to decide how much more water is needed.

At first notice that hectoliters is bigger than liters, which implies conversion of bigger unit to smaller unit has to be done.This means we need to multiply. There are 100 liters in a hectoliter, so the conversion factor becomes 100.

Now, take the given number of hectoliters and multiply by 100.

2.8 × 100 = 280 liters.

280 – 200 = 80 liters.

Therefore 80 more liters are required to fill the container completely.

**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.

2.8 hectoliter × 100 liters / 1 hectoliter

Step 2: Divide out the common units.

2.8 × 100 liters = 280 liters.

**Example 2: **To make a violet paint, Khan mixes 0.45 liter of red paint, 0.55 liter of blue paint, and 6.5 centiliters of white paint. How many centiliters of paint are in the mixture?

**Method: 1**

**Solution:** To add the quantity of each paint, they all must have same units. So, we convert red and blue paint to centiliters and then proceed to add.

At first notice that liters are bigger than centiliters, which implies conversion of bigger unit to smaller unit has to be done.This means we need to multiply. There are 100 centiliters in a liter, so the conversion factor becomes 100.

Red paint = 0.45 liter.

0.45 × 100 = 45 centiliter.

Blue paint = 0.55 liter.

0.55 × 100 = 55 centiliter.

Total quantity of paint = 6.5+45+55

= 106.5 centiliters.

**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.

Blue and red paint = 0.45+0.55

= 1.00 liter

1 liter × 100 centiliter/1 liter

Step 2: Divide out the common units.

1 × 100 centiliters = 100 centiliters.

The total quantity of the paint = 100 +6.5

= 106.5 centiliters.

**5.9.3 Convert metric units of mass**

**Example 1: **Chris has a collection of 25 footballs of same type, each weighing 120 grams. What is the total weight of all the balls in kilograms?

**Method: 1**

**Solution:** At first notice that grams are smaller than kilograms, which implies conversion of smaller unit to bigger unit has to be done.This means we need to divide. There are 1000 grams in a kilogram, so the conversion factor becomes 1000.

Weight of each ball = 120 grams.

Number of balls = 25.

Weight of all the balls = 25 × 120 grams = 3000 grams.

3000 grams ÷ 1000 = 3 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.

Weight of 25 balls = 3000 grams.

3000 grams × 1 kilogram/1000 grams

Step 2: Divide out the common units.

3000 kilogram ÷ 1000 = 3 kilograms.

**Example 2: **Convert 50 dekagrams to grams.

**Method: 1**

**Solution:** At first notice that dekagrams are bigger than grams, which implies conversion of bigger unit to smaller unit has to be done.This means we need to divide. There are 10 grams in a dekagram, so the conversion factor becomes 10.

Now, take the given number of dekagrams and multiply by 10.

50 × 10 = 500 grams.

**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.

50 dekagrams × 10 grams/ 1 dekagram

Step 2: Divide out the common units.

50 × 10 grams = 500 grams.

## Exercise:

1. Edward bought 90 liters of juice to distribute among his 15 friends. How much would each of his friend get in liters?

2. Shelly purchased 40 m and 200 cm long rope; how much is the length of the rope in terms of centimeters?

3. Maya used 13 m and SO cm of yellow ribbon and 20 m and 80 cm of blue ribbon. How much ribbon did she use in all in terms of dekameters?

4. Sara bought 500 ml of mustard oil, 250 ml of coconut oil and 2 liters of refined oil. What is the total quantity of oils together in centiliters?

5. An oil tank has 162 liters 345 ml oil. 78 liters 589 ml oil is removed from the tank. How much oil is left in the tank in terms of hectoliters.

6. A spray container holds 350 ml. Each spray releases 12 ml of spray. How much spray is left in the container in terms of centiliters if the spray was used for 12 times?

7. A box can hold 2 kg of weight. If 8 hectograms of clothes and half a kilogram of nuts are packed. How much more weight can be accommodated in the box in hectometers?

8. The weight of a package is SO decigrams containing forks each weighing 10 grams. If there are 35 forks, then how much weight more can be packed?

9. Rey has a bowl that contains 0.590 kilograms of sugar. He uses a spoon to remove 850 centigrams. How much sugar, in centigrams, remains?

10. James is a professional weightlifter. His personal lifting record was 125.3 kg. At the competition he broke his record by 540 grams. Express his new record in hectograms.

### What have we learned?

• Convert metric unit of lengths.

• Convert metric units of capacity.

• Convert metric units of mass.

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