Length and Its Metric Units

LESSON – MEASUREMENT

 

TOPIC

• Introduction

• Concept of Centimetres, Metres and Kilometres

• Conversion between Centimetres, Metres and Kilometres

• Addition and Subtraction of Length in Cm, M and Km

• Word Problems

 

INTRODUCTION 

Length is the measurement of distance from one point to other side of an object. 

Length is measured in centimetres and millimetres, metres and kilometres.

A kilometer (km), meter (m), and centimeter (cm) are the standard units of length. 

Centimetres and millimetres are used for measuring short distances while metres and kilometres are used for measuring long distances.

 

SYNONYMS FOR LENGTH 

Breadth (width) and height are commonly used as length.

 

RELATIONSHIP LENGTH, BREADTH AND HEIGHT 

Length refers how long is the object.

Breadth (width) refers how short is the object.

Height refers how tall is the object.

Length and breadth are used for 2 dimensional shapes while length, breadth and height are used for 3 dimensional shapes. 

 

CONCEPTS OF CENTIMETRES, METRES AND KILOMETRES 

• Centimeter (cm) is a metric unit of length that equals one hundredth of a meter. That’s, 100 cm = 1 m

•  Meter (m) is a metric unit of length that equals one hundred of a centimeter. That’s, 1 m = 100 cm.

• Kilometer (km) is a metric unit of length that’s equal to one thousand of a metres. That’s, 1 km = 1000 m

 

CONVERTING CM TO M (100 CM = 1 M) 

Working Example 1

Convert 100 cm to meters.

1st, divide the number of centimeters by 100,

100 ÷ 100 = 1

2nd, change the unit to meter.

100 cm = 1 m

 

Working Example 2 

Convert 253 cm to metre.

1st, divide the number of centimeters by 100,

253 ÷ 100 = 2.53

2nd, change the unit to meter.

253 cm = 2.53 m or 2 m 53 cm

 

Working Example 3

Convert 23 cm to metre.

1st, divide the number of centimeters by 100,

23 ÷ 100 = 0.23

2nd, change the unit to metre,

23 cm = 0.23 m

 

Working Example 4

Convert 9 cm to metre.

1st, divide the number of centimeters by 100,

9 ÷ 100 = 0.09

2nd, change the unit to metre,

9 cm = 0.09 m

 

WORKING EXERCISE 

Convert the following to metres,

1. 25 cm

2. 125 cm

3. 328

 

SOLUTIONS

1. 25 cm = 25 ÷ 100 = 0.25 m

2. 125 cm= 125 ÷ 100 = 1.25 m or 1 m 25 cm

3. 328 cm = 328÷ 100 = 3.28 m or 3 m or 28 cm

 

CONVERTING M TO CM (1 M = 100 CM) 

Working Example 1 

Convert 5 m to centimetres.

1st, multiply the number by 100,

5 x 100

2nd, change the unit to centimetres,

5 m = 500 m

 

Working Example 2 

Convert 2.3 m to centimetres.

1st, multiply the number by 100,

2.3 x 100 = 230

2nd, change the unit to centimetres,

2.3 m = 230 cm

 

Working Example 3

Convert 0.8 m to centimetres.

1st, multiply the number by 100,

0.8 x 100 = 80

2nd, change the unit to centimetres,

0.8 m = 80 cm

 

WORKING EXERCISES 

Convert the following to centimetres,

1. 11 m

2. 7.9 m

3. 0.61 m

 

SOLUTIONS

1. 11 m = 11 x 100 = 1100 cm

2. 7.9 m = 7.9 x 100 = 790 cm

3. 0.61 m = 0.61 x 100 = 61 cm

 

CONVERT M TO KM (0.001 M = 1 KM) 

Working Example 1

Convert 9000 m to kilometres.

1st, divide the number of metres by 1000,

9 000 ÷ 1000 = 9

2nd, change the unit to kilometres,

9 000 m = 9 km

 

Working Examples 2

Convert 632 m to kilometres.

1st, divide the number of metres by 1000,

632 ÷ 1000 = 0.632

2nd, change the unit to kilometres,

632 m = 0.632 km

 

Working Examples 3

Convert 52 m to kilometres.

1st, divide the number of metres by 1000,

52 ÷ 1000 = 0.052

2nd, change the unit to kilometres,

52 m = 0.052 km

 

Working Examples 4

Convert 6 m to kilometres.

1st, divide the number of metres by 1000,

6 ÷ 1000 = 0.006

2nd, change the unit to kilometres,

6 m = 0.006 km

 

WORKING EXERCISES 

Convert the following metre to centimetres,

1. 5 m

2. 25 m

3. 326 m

4. 1 020 m

 

SOLUTIONS

1. 5 m = 5 ÷ 1 000 = 0.005 km

2. 25 m = 25 ÷ 1 000 = 0.025 km

3. 326 m = 326 ÷ 1 000 = 0.326 km

4. 1 020 m = 1020 ÷ 1 000 = 1.02 km

 

CONVERT KM TO M (1 KM = 1 000 M) 

Woking Example 1

Convert 3 km to metres.

1st, multiply the number by 1 000,

3 x 1 000 = 3 000

2nd, change the unit to metres,

3 km = 3 000 m

 

Woking Example 2

Convert 1.5 km to metres.

1st, multiply the number by 1 000,

1.5 x 1 000 = 0.0015

2nd, change the unit to metres,

1.5 km = 0.0015 m

 

Woking Example 3

Convert 0.9 km to metres.

1st, multiply the number by 1 000,

0.9 x 1 000 = 900

2nd, change the unit to metres,

0.9 km = 900 m

 

WORKING EXERCISES 

Convert the following to metres,

1. 5 km

2. 6km 100 m

3. 0.78 km

 

SOLUTIONS

1. 5 km = 5 x 1 000 = 5 000 km

2. 6km 100 m = 6 x 1 000 + 100 = 6 000 + 100 = 6 100 m

3. 0.78 km = 0.78 x 1 000 = 780 km

 

ADDITION INVOLVING CM, M AND KM

Working Example 1 

A. Measure the following lines.

_______________________ cm

__________________________________________ cm

 

B. Add the two lines together.

C. Convert the result in B to metres.

 

SOLUTION

A. Lets assumed the lines is 58 cm and 73 cm respectively.

B. Add 58 cm and 73 cm

¹5 8 cm

+ 7 3 cm

_________

1 3 1 cm

C. Convert 131 cm to metre.

131 cm = 131 ÷ 100 = 1.31 = 1.31 m or 1 m 31 cm

 

Working Example 2 

Add 5 m 56 cm and 8 m 69 cm

¹5 m 56 cm

+ 8 m 59 cm

______________

14 m 05 cm

 

Working Example 3

Add 5 km 674 m and 3 km 475 m together.

¹5 km ¹674 m

+ 3 km 475 m

______________

9 km 149 m

 

WORKING EXERCISES 

Add the following:

1. 9 125 m and 6 786 m

2. 4 804 m, 3.498 km and 2 397 m

3. 989 m and 483 m

4. 2.168 km + 700 m

5. 6 m 71 cm and 5 m 92 cm

 

SOLUTIONS

1. 9 125 m and 6 786 m

9 125 m

+ 6 786 m

______________

15 911 m

Therefore, 9 125 m + 6 786 m = 15 911 m or 15 km 912 m or 15.912 km

 

2. 4 804 m, 3.498 km and 2 397 m

¹4 804 m

(3.498 km = 3 498 m), + 3 498 m

+ 2 397 m

______________

10 699 m

Therefore, 4 804 m + 3.498 km + 2 397 m = 10 699 m or 10 km 699 m or 10.699 km

 

3. 989 m and 483 m

¹989 m

+ 483 m

______________

1 472 m

Therefore, 989 m + 483 m = 1 472 m or 1 km 483 m or 1.472 km

 

4. 2.168 km + 700 m

2.168 km

(700 m = 0.700 km) + 0.700 km

______________

2.868 km

Therefore, 2.168 km + 700 m = 2.878 km or 2 km 878 m or 2 878 m

 

5. 6 m 71 cm + 5 m 92 cm

¹6 m 71 cm

+ 5 m 92 cm

______________

12 m 63 cm

Therefore, 6 m 71 cm + 5 m 92 cm = 12 m 63 cm or 12.63 m or 1 263 cm

 

SUBTRACTION INVOLVING CM, M AND KM

Working Example 1

Subtract 9 m 56 cm and 8 m 69 cm

9 m 56 cm

+ 8 m 59 cm

______________

97 cm

Therefore, 9 m 56 cm – 8 m 69 cm = 97 cm or 0.97 m

 

Working Example 2

4 804 m + 3.498 km – 2 397 m

4 804 m

(3.498 km = 3 498 m), + 3 498 m

______________

8 302 m

– 2 397 m

______________

5 905 m

 

Therefore, 4 804 m + 3.498 km – 2 397 m = 5 905 m or 5 km 905 m or 5.905 km

 

Working Example 3

989 m – 483 m

989 m

– 483 m

______________

506 m

Therefore, 989 m – 483 m = 506 m or 5.06 km

 

Working Example 4

2.168 km – 700 m

2.168 km

(700 m = 0.700 km) – 0.700 km

______________

1.468 km

Therefore, 2.168 km – 700 m = 1.468 km or 1 km 468 cm

 

WORD PROBLEMS

Word problems are mathematical problems presented a simple language rather than in mathematical notation.

 

Working Example 1 

A man travels from Lagos to Ibadan in 15.7 km, Ibadan to Ilorin in 29.1 km and Ilorin to Abuja 34.9 km.

• What is the total distance traveled?

• Find the average distance traveled.

 

Solution,

Total distance is,

15.7 km

+ 29.1 km

+ 34.9 km

____________

79.7 km

Average distance is,

79.7

              _______ 26.6 km

3

 

Working Example 2

A man walks 150 kilometres in 5 hours. How long does he work in,

• 3 hours

• 8 hours

• 12 hours

 

Solution,

In one hour, he walks in

150

              _________ = 30 km

5

• In 3 hours, 3 x 30 = 90 km

• In 8 hours, 8 x 30 = 240 km

• In 12 hours, 12 x 30 = 360 km

 

Working Example 3

A boy can walk a distance of 100 km in 20 hours . Find the average distance.

100

              _________ = 5 km

20

 

WORKING EXERCISES 

1. A man travels from Lagos to Ilorin in 25.7 km, Ilorin to Abuja in 79.1 km and Ilorin to Kaduna 64.9 km.

• What is the total distance traveled?

• Find the average distance traveled.

2. A man can walk a distance of 280 km in 12 hours . Find the average distance.

 

3. A man walks 360 kilometres in 5 hours. How long does he work in,

• 3 hours

• 8 hours

• 12 hours