We will discuss here about the metric measures of length, mass and capacity.

Measurements of length, mass and capacity:

We know about the different units for measuring length, mass and capacity. We also know about the relationship between the units.

Let us revise them.

Length is measured in kilometre, metre and centimetre.

Mass is measured in kilogram and gram.

Capacity is measured in litre and millilitre.

You know that

**1 metre = 100 centimetres**

**1 kilometre = 1000 metres**

**1 kilogram = 1000 grams**

**1 litre = 1000 millilitres**

The basic unit of length is metre, the basic unit of mass is kilogram and the basic unit of capacity is litre. This system of measurement of length, mass and capacity is known as Metric system.

In metric system, we represent thousands by kilo, hundreds by hector, tens by deca, tenths by deci, hundredths by centi and thousandths by milli. This system is decimal since each unit is 10 times the next smaller unit.

As we know, the standard units of length, weight and capacity are metre (m), gram (g) and litre (l) respectively. Kilometre (km) kilogram (kg) and kilolitre (kl) are the bigger units of length, weight and capacity respectively. The three-basic unit systems of measurement of length, mass and capacity is known as metric system.

This is decimal system based on the multiples of 10.

** Measures of Length**

10 millimetres (mm) 10 centimetres 10 decimetres 10 metres 10 decametres 10 hectometres |
= = = = = = |
1 centimetre (cm) 1 decimetre (dm) 1 metre (m) 1 decametre (dam) 1 hectometre (hm) 1 kilometre (km) |

** Measures of Weight**

10 milligrams (mg) 10 centigrams 10 decigrams 10 grams 10 decagrams 10 hectograms |
= = = = = = |
1 centigram (cg) 1 decigram (dg) 1 gram (g) 1 decagram (dag) 1 hectogram (hg) 1 kilogram (kg) |

**Note:**

100 kg = 1 quintal

10 quintals = 1 tonne

1000 kg = 1 tonne

** Measures of Capacity**

10 millilitres (ml) 10 centilitres 10 decilitres 10 litres 10 decalitres 10 hectolitres |
= = = = = = |
1 centilitre (cl) 1 decilitre (dl) 1 litre (l) 1 decalitre (dal) 1 hectolitre (hl) 1 kilolitre (kl) |

We can understand the metric system more clearly through the following table of metric measures.

Thousand 1000 |
Hundred 100 |
Ten 10 |
One 1 |
Tenth 1/10 |
Hundredth 1/100 |
Thousandth 1/1000 | |

Metric Unit |
Kilo (x1000) |
Hecto (x100) |
Deca (x10) |
Basic Unit |
Deci (÷ 10) |
Centi (÷ 100) |
Milli (÷ 100) |

Mass |
Kilo- gram |
Hecto- gram |
Deca- gram |
Gram |
Deci- gram |
Centi- gram |
Milli- gram |

Length |
Kilo- metre |
Hecto- metre |
Deca- metre |
Metre |
Deci- metre |
Centi- metre |
Milli- metre |

Capacity |
Kilo- litre |
Hecto- litre |
Deca- litre |
Litre |
Deci- litre |
Centi- litre |
Milli- litre |

Measurement of length, mass and capacity tables can be represented in the form of a place-value chart as shown below.

From the above table of metric system we come to know that:

Deca means 10 times

Hecto means 100 times

Kilo means 1000 times

These are the bigger units of metric system

Deci means \(\frac{1}{10}\) times

Centi means \(\frac{1}{100}\) times

Millimeans \(\frac{1}{1000}\) times

These are the smaller units of metric system

**Questions and Answers on Metric Measures:**

**I.** Convert 1629 grams into

(i) kilograms

(ii) hectograms

(iii) decagrams

**Answer: **

**I.** (i) 1.629 kilograms

(ii) 16.29 hectograms

(iii) 162.9 decagrams

**II.** Convert 4525 millilitres into

(i) litres

(ii) decilitres

(iii) centilitres

**Answer:**

**II.** (i) 4.525 litres

(ii) 45.25 decilitres

(iii) 452.5 centilitres

**III.** Convert 4020 metres into

(i) kilometres

(ii) hectometres

(iii) decametres

**Answer:**

**III.** (i) 4.02 kilometres

(ii) 40.2 hectometres

(iii) 402 decametres

**IV.** Convert 1756 kilograms into

(i) quintals

(ii) tonnes

**Answer:**

**IV.** Convert 1756 kilograms into

(i) quintals

(ii) tonnes

**V.** Convert 726 quintals into tonnes

**VI.** Convert 125 kilometres into

(i) hectometres

(ii) decametres

(iii) metres

**VII.** Convert 75 kilograms into

(i) decigrams

(ii) centigrams

(iii) milligrams

**VIII.** Convert 120 litres into

(i) kilolitres

(ii) decalitres

(iii) decilitres

(iv) millilitres

**IX.** Convert 7 tonnes into

(i) kilograms

(ii) quintals

**X.** Convert 825 quintals into kilograms.

**XI. Fill in the blanks:**

(i) 5 kg 600 g = 4 kg ……… g

(ii) 3 hm 20 m = ……… m

(iii) 6 hl 4 dal = ……… l

(iv) 5 m 6 dm = ……… cm

(v) 1 km 2 hm 3 dam 2 m = ……… m

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