Measurement of Length, Mass and Volume: Metric Units, Conversions and Multiplication

Measurement of Length, Mass and Volume

1.1 Introduction to Multiplication of Metric Units

In everyday life, we measure the length of roads, the mass of goods in a market, and the volume of water in a tank. These measurements are made using the metric system. The metric system is a decimal system — all units are related by multiples of 10, 100, or 1,000. This makes it easy to convert between units by multiplying or dividing.

Key Metric Relationships to Remember

Metric Unit	Conversions
Length	1 km = 1,000 m \| 1 m = 100 cm \| 1 cm = 10 mm
Mass	1 tonne = 1,000 kg \| 1 kg = 1,000 g \| 1 g = 1,000 mg
Volume	1 l = 1,000 ml

Multiplication of metric units means multiplying a measurement by a whole number. For example, if one bag of rice has a mass of 2 kg, then 5 bags have a mass of 5 × 2 kg = 10 kg.

When multiplying metric units, multiply the number and keep the unit. If the result is large enough, you can convert to a bigger unit.

Example 1: Multiply: 3 × 4 km

Step 1: Multiply the numbers: 3 × 4 = 12
Step 2: Keep the unit.

Answer: 12 km

Example 2: Multiply: 5 × 250 m

Step 1: Multiply: 5 × 250 = 1,250
Step 2: 1,250 m ÷ 1,000 = 1 remainder 250
Step 3: Convert: 1,250 m = 1 km 250 m

Answer: 1 km 250 m

Example 3: Multiply: 6 × 3 kg 200 g

Step 1: Multiply the kg: 6 × 3 kg = 18 kg
Step 2: Multiply the g: 6 × 200 g = 1,200 g
Step 3: Convert 1,200 g: 1,200 ÷ 1,000 = 1 kg remainder 200 g
Step 4: Add: 18 kg + 1 kg 200 g = 19 kg 200 g

Answer: 19 kg 200 g

Example 4: Multiply: 4 × 2 l 500 ml

Step 1: Multiply litres: 4 × 2 = 8 l
Step 2: Multiply ml: 4 × 500 = 2,000 ml
Step 3: Convert 2,000 ml: 2,000 ÷ 1,000 = 2 l
Step 4: Add: 8 l + 2 l = 10 l

Answer: 10 l

1.2 Measurement of Length

Length is the measurement of how long, tall, or far apart things are. We use a ruler, tape measure, or metre rule to measure length. The standard unit of length in the metric system is the metre (m).

Units of Length (from smallest to largest)

Millimetre (mm) → Centimetre (cm) → Metre (m) → Kilometre (km)

10 mm = 1 cm
100 cm = 1 m
1,000 m = 1 km

Figure 1.1: A ruler showing millimetres and centimetres

When measuring length:

Place the zero mark of the ruler at one end of the object.
Read the measurement at the other end of the object.
Record the measurement with the correct unit.

Example 1: A pencil measures 14 cm 5 mm. Write this in mm only.

Step 1: Convert cm to mm: 14 cm × 10 = 140 mm
Step 2: Add the remaining mm: 140 mm + 5 mm = 145 mm

Answer: 145 mm

Example 2: A rope is 3 m 45 cm long. Write this in cm only.

Step 1: Convert m to cm: 3 × 100 = 300 cm
Step 2: Add remaining cm: 300 + 45 = 345 cm

Answer: 345 cm

Example 3: Write 2,500 m in km and m.

Step 1: Divide by 1,000: 2,500 ÷ 1,000 = 2 remainder 500
Step 2: 2,500 m = 2 km 500 m

Answer: 2 km 500 m

Example 4: A room is 4 m 60 cm wide and 5 m 30 cm long. Find the total length of two walls (one width + one length).

Step 1: Add: 4 m 60 cm + 5 m 30 cm
Step 2: Add cm: 60 + 30 = 90 cm
Step 3: Add m: 4 + 5 = 9 m
Step 4: Total = 9 m 90 cm

Answer: 9 m 90 cm

Practice Questions

Convert 3 km to metres.
Convert 450 cm to metres and centimetres.
Write 67 mm in cm and mm.
A table is 1 m 80 cm long. Write this length in cm.
A road is 5 km 300 m long. Write this length in metres only.
Express 2,050 mm in metres and centimetres.
Convert 8 m 75 cm to centimetres.
A shelf is 920 mm wide. Write in cm and mm.
Write 4 km 50 m in metres only.
How many millimetres are in 3 cm 7 mm?

1.3 Measuring Length of Various Objects

We measure different objects using appropriate tools and units. Short objects like pencils and books are measured in centimetres (cm) or millimetres (mm). Longer objects like rooms and fields are measured in metres (m). Very long distances like roads and railway lines are measured in kilometres (km).

Figure 1.2: Using a tape measure to measure the length of a classroom

Choosing the Right Unit

Object or Distance	Appropriate Unit
Thickness of a coin	millimetres (mm)
Length of a pencil / book	centimetres (cm)
Width / length of a room	metres (m)
Distance between two towns	kilometres (km)

Example 1: A mathematics textbook is 28 cm 5 mm long. How long is it in mm?

Step 1: 28 cm × 10 = 280 mm
Step 2: 280 + 5 = 285 mm

Answer: 285 mm

1.4 Multiplication of Length

Multiplying length means finding the total length when the same measurement is repeated a number of times. For example, if a room is 4 m 50 cm long, then 3 such rooms placed end to end would have a total length of 3 × 4 m 50 cm.

Steps for Multiplying Length with Two Units (e.g., m and cm):

Multiply the smaller unit (cm or mm) first.
If the result is 100 cm or more, convert to metres (divide by 100).
Multiply the larger unit (m or km).
Add the converted amount to the larger unit.

Example 1: Multiply: 3 × 5 m 20 cm

Step 1: Multiply cm: 3 × 20 = 60 cm (less than 100, no conversion needed)
Step 2: Multiply m: 3 × 5 = 15 m
Step 3: Combine: 15 m 60 cm

Answer: 15 m 60 cm

Example 2: Multiply: 4 × 2 m 75 cm

Step 1: Multiply cm: 4 × 75 = 300 cm
Step 2: Convert 300 cm: 300 ÷ 100 = 3 m, 0 cm remaining
Step 3: Multiply m: 4 × 2 = 8 m
Step 4: Add: 8 m + 3 m 0 cm = 11 m

Answer: 11 m

Example 3: Multiply: 6 × 3 km 250 m

Step 1: Multiply m: 6 × 250 = 1,500 m
Step 2: Convert: 1,500 ÷ 1,000 = 1 km 500 m
Step 3: Multiply km: 6 × 3 = 18 km
Step 4: Add: 18 km + 1 km 500 m = 19 km 500 m

Answer: 19 km 500 m

Example 4: Multiply: 5 × 8 cm 6 mm

Step 1: Multiply mm: 5 × 6 = 30 mm
Step 2: Convert 30 mm: 30 ÷ 10 = 3 cm, 0 mm
Step 3: Multiply cm: 5 × 8 = 40 cm
Step 4: Add: 40 cm + 3 cm = 43 cm

Answer: 43 cm

1.5 Word Problems on Length

Word problems require you to read carefully, identify the key information, decide which operation to use (addition, subtraction, multiplication, or division), carry out the calculation, and write a clear answer with units.

Steps for Solving Word Problems

Step 1: Read the problem carefully.
Step 2: Identify what you are given and what you need to find.
Step 3: Choose the correct operation (+, -, ×, ÷).
Step 4: Perform the calculation.
Step 5: Write the answer in a complete sentence with the correct unit.

Example 1: A farmer has 4 pieces of rope, each 3 m 25 cm long. What is the total length of all four pieces?

Step 1: Operation → Multiplication (same length repeated)
Step 2: Multiply cm: 4 × 25 = 100 cm = 1 m
Step 3: Multiply m: 4 × 3 = 12 m
Step 4: Add: 12 m + 1 m = 13 m

Answer: The total length of rope is 13 m.

Example 2: The distance from Juma's house to school is 2 km 400 m. If he walks to school and back every day, how far does he walk in 5 days?

Step 1: Distance for one trip = 2 km 400 m

Step 2: Distance per day (there and back) = 2 × 2 km 400 m

Multiply m: 2 × 400 = 800 m
Multiply km: 2 × 2 = 4 km

Per day: 4 km 800 m

Step 3: For 5 days: 5 × 4 km 800 m

Multiply m: 5 × 800 = 4,000 m = 4 km
Multiply km: 5 × 4 = 20 km

Total: 20 + 4 = 24 km

Answer: Juma walks 24 km in 5 days.

Example 3: A piece of cloth is 10 m long. A tailor cuts off 3 m 85 cm. How much cloth is left?

Step 1: Operation → Subtraction
Step 2: Convert 10 m to 9 m 100 cm (borrow 1 m)
Step 3: Subtract cm: 100 - 85 = 15 cm
Step 4: Subtract m: 9 - 3 = 6 m
Step 5: Remaining cloth = 6 m 15 cm

Answer: 6 m 15 cm of cloth is left.

1.7 Multiplication of Mass and Word Problems

Just like multiplying length, we multiply mass when the same mass is repeated a number of times. The method is the same: multiply the smaller unit first, convert if necessary, then multiply the larger unit and add.

Example 1: Multiply: 4 × 2 kg 300 g

Step 1: Multiply g: 4 × 300 = 1,200 g
Step 2: Convert 1,200 g: 1,200 ÷ 1,000 = 1 kg 200 g
Step 3: Multiply kg: 4 × 2 = 8 kg
Step 4: Add: 8 kg + 1 kg 200 g = 9 kg 200 g

Answer: 9 kg 200 g

Example 2: Multiply: 6 × 1 t 400 kg

Step 1: Multiply kg: 6 × 400 = 2,400 kg
Step 2: Convert: 2,400 ÷ 1,000 = 2 t 400 kg
Step 3: Multiply t: 6 × 1 = 6 t
Step 4: Add: 6 t + 2 t 400 kg = 8 t 400 kg

Answer: 8 t 400 kg

Example 3: A sack of beans has a mass of 50 kg 500 g. What is the total mass of 3 such sacks?

Step 1: 3 × 50 kg 500 g
Step 2: Multiply g: 3 × 500 = 1,500 g = 1 kg 500 g
Step 3: Multiply kg: 3 × 50 = 150 kg
Step 4: Add: 150 kg + 1 kg 500 g = 151 kg 500 g

Answer: Total mass = 151 kg 500 g

Example 4: 5 packets of flour each weigh 2 kg 800 g. What is the total mass?

Step 1: 5 × 2 kg 800 g
Step 2: Multiply g: 5 × 800 = 4,000 g = 4 kg
Step 3: Multiply kg: 5 × 2 = 10 kg
Step 4: Add: 10 + 4 = 14 kg

Answer: Total mass = 14 kg

Example 5: A truck makes 7 trips, carrying 2 t 600 kg of sand each trip. What is the total mass of sand carried?

Step 1: 7 × 2 t 600 kg
Step 2: Multiply kg: 7 × 600 = 4,200 kg = 4 t 200 kg
Step 3: Multiply t: 7 × 2 = 14 t
Step 4: Add: 14 t + 4 t 200 kg = 18 t 200 kg

Answer: Total mass = 18 t 200 kg

Measurement of Length, Mass and Volume: Metric Units, Conversions and Multiplication - Grade 5 Notes