# 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 1Convert 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 2Convert 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 3Convert 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 4Convert 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 EXERCISEConvert the following to metres,

1. 25 cm

2. 125 cm

3. 328

SOLUTIONS1.

25 cm= 25 ÷ 100 =0.25 m

2.

125 cm= 125 ÷ 100 =1.25 mor1 m 25 cm3.

328 cm= 328÷ 100 =3.28 mor3 m or 28 cm

**CONVERTING M TO CM (1 M = 100 CM) **

Working Example 1Convert 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 2Convert 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 3Convert 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 EXERCISESConvert the following to centimetres,

1. 11 m

2. 7.9 m

3. 0.61 m

SOLUTIONS1.

11 m= 11 x 100 =1100 cm2.

7.9 m= 7.9 x 100 =790 cm3.

0.61 m= 0.61 x 100 =61 cm

**CONVERT M TO KM (0.001 M = 1 KM) **

Working Example 1Convert 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 3Convert 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 4Convert 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 EXERCISESConvert the following metre to centimetres,

1. 5 m

2. 25 m

3. 326 m

4. 1 020 m

SOLUTIONS1.

5 m= 5 ÷ 1 000 =0.005 km2.

25 m= 25 ÷ 1 000 =0.025 km3.

326 m= 326 ÷ 1 000 =0.326 km4.

1 020 m= 1020 ÷ 1 000 =1.02 km

**CONVERT KM TO M (1 KM = 1 000 M) **

Woking Example 1Convert 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 2Convert 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 3Convert 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 EXERCISESConvert the following to metres,

1. 5 km

2. 6km 100 m

3. 0.78 km

SOLUTIONS1. 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 1A. Measure the following lines.

_______________________ cm

__________________________________________ cm

B. Add the two lines together.

C. Convert the result in B to metres.

SOLUTIONA. 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 mor1 m 31 cm

Working Example 2Add 5 m 56 cm and 8 m 69 cm

¹5 m 56 cm

+ 8 m 59 cm

______________

14 m 05 cm

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

¹5 km ¹674 m

+ 3 km 475 m

______________

9 km 149 m

WORKING EXERCISESAdd 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

SOLUTIONS1. 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 mor15 km 912 mor15.912 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 mor10 km 699 mor10.699 km

3. 989 m and 483 m

¹989 m

+ 483 m

______________

1 472 m

Therefore, 989 m + 483 m =

1 472 mor1 km 483 mor1.472 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 cmor12.63 mor1 263 cm

**SUBTRACTION INVOLVING CM, M AND KM**

Working Example 1Subtract 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 24 804 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 3989 m – 483 m

989 m

– 483 m

______________

506 m

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

Working Example 42.168 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 1A 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 2A 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 3A boy can walk a distance of 100 km in 20 hours . Find the average distance.

100

_________ = 5 km

20

WORKING EXERCISES1. 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