Class 5 Maths

Measurement of Length – Class 5 Mathematics

Measurement of Length

In this chapter – Measurement of Length for Class 5, we will be solving problems involving length. We will learn to convert smaller units of length into bigger units and bigger units into smaller units. Let’s learn some basic facts first.

Conversion of Smaller Units into Bigger Units

(A) 10 millimetres (mm) = 1 centimetre (cm)

or, 10 mm = 1 cm

Therefore, \text{1 mm =} \cfrac{1}{10} \text{ cm =} \text{0.1 cm}

Remember: 1 mm is one-tenth of 1 cm

Some more examples,

5 mm = \cfrac{5}{10} \text{ cm = 0.5 cm}

9 mm = \cfrac{9}{10} \text{ cm = 0.9 cm}

So, to convert mm into cm, divide the mm by 10.

(B) 10 centimetres (cm) = 1 decimetre (dm)

or, 10 cm = 1 dm

Therefore, \text{1 cm = } \cfrac{1}{10} \text{ dm = 0.1 dm}

Remember: 1 cm is one-tenth of 1 dm

Some more examples,

3 cm = \cfrac{3}{10} \text{ dm = 0.3 dm}

8 cm = \cfrac{8}{10} \text{ dm = 0.8 dm}

So, to convert cm into dm, divide the cm by 10

(C) 10 decimetres (dm) = 1 metre (m) or, 10 dm = 1 m

Therefore, \text{1 dm = } \cfrac{1}{10} \text{ m = 0.1 m}

Remember: 1 dm is one-tenth of 1 m

Some more examples,

2 cm = \cfrac{2}{10} \text{ m = 0.2 m}

9 cm = \cfrac{9}{10} \text{ m = 0.9 m}

So, to convert cm into dm, divide the cm by 10

(D) 100 centimetres (cm) = 1 metre (m)

or, 100 cm = 1 m

Therefore, \text{1 cm = } \cfrac{1}{100} \text{ m = 0.01 m}

Remember: 1 cm is one-hundredth of 1 m

Some more examples,

25 cm = \cfrac{25}{100} \text{ m = 0.25 m}

50 cm = \cfrac{50}{100} \text{ m = 0.50 m}

So, to convert cm into m, divide the cm by 100

(E) 1000 metres (m) = 1 kilometre (km)

or, 1000 m = 1 km

\therefore \text{1 m = } \cfrac{1}{1000} \text{ km = 0.001 km}

Remember: 1 m is one-thousandth of 1 km

Some more examples,

50 m = \cfrac{50}{1000} \text{ km = 0.050 km or 0.05 km}

99 m = \cfrac{99}{1000} \text{ km = 0.099 km}

655 m = \cfrac{655}{1000} \text{ km = 0.655 km}

So, to convert m into km, divide the m by 1000

Solved Examples

Example 1:
Convert 7 mm into cm

7 mm = \cfrac{7}{10} \text{cm = 0.7 cm}

Example 2:
Convert 15 cm into m

15 cm = \cfrac{15}{100} \text{m = 0.15 m}

Example 3:
Convert 20 dm into m

20 dm = \cfrac{20}{10} \text{m = 2 m}

Example 4:
Convert 375 m into km

375 m = \cfrac{375}{1000} \text{km = 0.375 km}

Example 5:
Convert 75 m into km

75 m = \cfrac{75}{1000} \text{km = 0.075 km}

Example 6:
Convert 5 cm 9 mm into cm

5 cm 9 mm = 5 cm + 9 mm = 5 cm + 0.9 cm = 5.9 cm

Example 7:
Convert 2 km 5 m into km

2 km 5 m = 2 km + 5 m = 2 km + 0.005 km = 2.005 km

Conversion of Bigger Units into Smaller Units

We have learned that

  • 1 cm = 10 mm
    5 cm = = 5 x 10 mm = 50 mm
    7.5  cm = 7.5 x 10 mm = 7.5 mm
  • 1 m = 10 dm
    8 m = 8 x 10 dm = 80 dm
    6.2 m = 6.2 x 10 dm = 62 dm
  • 1 m = 100 cm
    3 m = 3 x 100 cm = 300 cm
    5.5 m = 5.5 x 100 cm = 550 cm
  • 1 km = 1000 m
    9 km = 9 x 1000 m = 9000 m
    6.2 km = 6.2 x 1000 m = 6200 m

Solved Examples

Example 8:
Convert 7.5 m into cm

7.5 m = 7.5 x 100 cm = 750 cm

Example 9:
Convert 7.5 m into m and cm

7.5 m = 7 m + 0.5 m = 7 m + 0.5 x 100 cm = 7 m + 50 cm = 7 m 50 cm

Example 10:
Convert 5.05 km into km and m

5.05 km = 5 km + 0.05 km = 5 km + 0.05 x 1000 m = 5 km + 50 m = 5 km 50 m

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