The system of measurement is called the Metric System.
(a) Meter is used for measuring Lenght.
(b) Gram is used for measuring Mass or Weight.
(c) Liter is used for measuring a Capacity.
Table of Units:
(a) Kilo - 1000
(b) Hecto - 100
(c) Deca - 10
(d) Metre, Gram or Litre - 1
(e) Deci - $\dfrac{1}{10}$ or 0.1
(f) Centi - $\dfrac{1}{100}$ or 0.01
(g) Milli - $\dfrac{1}{1000}$ or 0.001
For Distance or Lenght:
(a) 10 millimetres = 1 centimetre
(b) 10 centimetres = 1 decimetre
(c) 10 decimetres = 1 metre
(d) 10 metres = 1 decametre
(e) 10 decametres = 1 hectometre
(f) 10 hectometres = 1 kilometre
Relationship between measures of Distance or lenght:
(a) 1 kilometre = 1000 metres
(b) 1 metre = 100 centimetres
(c) 1 metre = 1000 millimetres
(d) 1 centimetre - 10 millimetres
More Relationship between measures of Distance or lenght:
(a) 1 kilometre = 1000 metres
(b) 1 hectometre = 100 metres
(c) 1 decametre = 10 metres
(d) 1 decimetre = $\dfrac{1}{10}$ or 0.1 metres
(e) 1 centimetre = $\dfrac{1}{100}$ or 0.01 metres
(f) 1 millimetre = $\dfrac{1}{1000}$ or 0.001 metres
For Mass or Weight:
(a) 10 milligrams = 1 centigram
(b) 10 centigrams = 1 decigram
(c) 10 decigrams = 1 gram
(d) 10 grams = 1 decagram
(e) 10 decagrams = 1 hectogram
(f) 10 hectograms = 1 kilogram
Relationship between measures of Mass or Weight:
(a) 1 kilogram = 1000 grams
(b) 1 gram = 100 centigrams
(c) 1 gram = 1000 milligrams
(d) 1 centigram - 10 milligrams
More Relationship between measures of Mass or Weight:
(a) 1 kilogram = 1000 grams
(b) 1 hectogram = 100 grams
(c) 1 decagram = 10 grams
(d) 1 decigram = $\dfrac{1}{10}$ or 0.1 grams
(e) 1 centigram = $\dfrac{1}{100}$ or 0.01 grams
(f) 1 milligram = $\dfrac{1}{1000}$ or 0.001 grams
For Capacity or Litre:
(a) 10 millilitres = 1 centilitre
(b) 10 centilitres = 1 decilitre
(c) 10 decilitres = 1 litre
(d) 10 litres = 1 decalitre
(e) 10 decalitres = 1 hectolitre
(f) 10 hectolitres = 1 kilolitre
Relationship between measures of Capacity or Litre:
(a) 1 kilolitre = 1000 litres
(b) 1 litre = 100 centilitres
(c) 1 litre = 1000 millilitres
(d) 1 centilitre - 10 millilitres
More Relationship between measures of Capacity or Litre:
(a) 1 kilolitre = 1000 litres
(b) 1 hectolitre = 100 litres
(c) 1 decalitre = 10 litres
(d) 1 decilitre = $\dfrac{1}{10}$ or 0.1 litres
(e) 1 centilitre = $\dfrac{1}{100}$ or 0.01 litres
(f) 1 millilitre = $\dfrac{1}{1000}$ or 0.001 litres
Conversion of unit of measurement:
Under the metric system, conversion of units is simple. To convert a given unit into a higher unit, we divide by 10, 100 or 1000. To convert a given unit into some smaller unit, we multiply it by 10, 100 or 1000.
Converting smaller to higher unit:
Eg. Convert 5864 centimetres into metres.
Solution: we know that 1 metre = 100 centimetres
$\therefore \dfrac{5864}{100}$ = 58.64 metres
Eg. Convert 5864 millimetres into metres.
Solution: we know that 1 metre = 1000 millimetres
$\therefore \dfrac{5864}{1000}$ = 5.864 metres
Eg. Convert 25 grams into kilograms.
Solution: we know that 1 kilogram = 1000 grams
$\therefore \dfrac{25}{1000}$ = 0.025 kilograms
Eg. Convert 50 litres into hectolitres.
Solution: we know that 1 hectolitre = 100 litres
$\therefore \dfrac{50}{1000}$ = 0.50 kilolitres
Converting higher to smaller unit:
Eg. Convert 50 grams into centigrams.
Solution: we know that 1 gram = 100 centigrams
$\therefore$ 50 $\times$ 100 = 5,000 centigrams
Eg. Convert 4 kilometres into metres.
Solution: we know that 1 kilometres = 1000 metres
$\therefore$ 4 $\times$ 1000 = 4,000 metres
Eg. Convert 30 litres into millilitres.
Solution: we know that 1 litre = 1000 millilitres
$\therefore$ 30 $\times$ 1000 = 30,000 millilitres
Under unit conversion, the decimal point is suitably shifted. When dividing, the decimal point is shifted towards the left. In multiplication, the decimal point is shifted towards the right.
Eg. Convert 3.4876 metres into decimetres, centimetres and millimetres.
Solution: we know that 1 metre = 10 decimetres
$\therefore \dfrac{34876}{10000}\times$ 10 = $\dfrac{3487}{1000}$ = 34.876 decimetres
we know that 1 metre = 100 centimetres
$\therefore \dfrac{34876}{10000}\times$ 100 = $\dfrac{3487}{100}$ = 348.76 centimetres
we know that 1 metre = 1000 millimetres
$\therefore \dfrac{34876}{10000}\times$ 1000 = $\dfrac{3487}{10}$ = 3487.6 millimetres
Eg. Convert 56.65 grams into decagrams, hectograms and kilograms.
Solution: we know that 10 grams = 1 decagram
$\therefore \dfrac{5665}{100 \times 10}$ = $\dfrac{5665}{1000}$ = 5.665 decagrams.
we know that 100 grams = 1 hectogram
$\therefore \dfrac{5665}{100 \times 100}$ = $\dfrac{5665}{10000}$ = 0.5665 hectograms.
we know that 1000 grams = 1 kilogram
$\therefore \dfrac{5665}{100 \times 1000}$ = $\dfrac{5665}{100000}$ = 0.05665 kilograms.
Some more examples:
Eg. Express 378 metres as decametre and metre.
Solution: $\therefore$ 378 metres = $\dfrac{370}{10}$ + 8 = 37 decametre and 8 metres.
Eg. Express 4235 grams as kilogram, hectogram, decagram and gram.
Solution: $\therefore$ 4235 grams = $\dfrac{4000}{1000}$ + $\dfrac{200}{100}$ + $\dfrac{30}{10}$ + 5
$\therefore$ 4 kilogram 2 hectogram 3 decagram and 5 grams.
Eg. Express 5 litres, 8 decilitres, 2 centilitres and 3 millilitres into millilitres.
$\therefore$ (5 $\times$ 1000) + (8 $\times$ 100) + (2 $\times$ 10) + (3 $\times$ 1)
$\therefore$ 5823 millimetres.
What is Estimation?
It is the process to make a fair guess. It provides a rough idea instead of an exact one.
Eg. 83 is about 80 and 98 is about 100. The guess result is 180 while the exact result is 181. The existing difference of 1 expresses a minute deviation. "Approximately" and "About" are the two most often used terms in Estimation. it is usually done by rounding off a given number to nearest 10, 100 or 1000. in case the given number is a middle one (5) then it is rounded to the nearest bigger number.
Eg. 125 is about 100
$\therefore$ 25 is about 30
$\therefore$ 175 is about 200
Question. If it takes 2 steps for a man to cover 2 meters then in how many steps will he be able to cover a distance of 1.5 kms.
Solution:
$\Rightarrow$ 1 km = 1000 meters
$\Rightarrow$ 1.5 kms = 1500 meters
$\Rightarrow$ Given, steps taken to cover 1 meter = $2$ steps
$\Rightarrow$ Steps taken to cover 100 meter = $2 \times 100 = 200$ steps
$\Rightarrow$ Steps taken to cover 1000 meter = $2 \times 1000 = 2000$ steps
$\therefore$ Steps taken to cover 1500 meter = $2 \times 1500 = 3000 $ steps Answer
(a) Meter is used for measuring Lenght.
(b) Gram is used for measuring Mass or Weight.
(c) Liter is used for measuring a Capacity.
Table of Units:
(a) Kilo - 1000
(b) Hecto - 100
(c) Deca - 10
(d) Metre, Gram or Litre - 1
(e) Deci - $\dfrac{1}{10}$ or 0.1
(f) Centi - $\dfrac{1}{100}$ or 0.01
(g) Milli - $\dfrac{1}{1000}$ or 0.001
For Distance or Lenght:
(a) 10 millimetres = 1 centimetre
(b) 10 centimetres = 1 decimetre
(c) 10 decimetres = 1 metre
(d) 10 metres = 1 decametre
(e) 10 decametres = 1 hectometre
(f) 10 hectometres = 1 kilometre
Relationship between measures of Distance or lenght:
(a) 1 kilometre = 1000 metres
(b) 1 metre = 100 centimetres
(c) 1 metre = 1000 millimetres
(d) 1 centimetre - 10 millimetres
More Relationship between measures of Distance or lenght:
(a) 1 kilometre = 1000 metres
(b) 1 hectometre = 100 metres
(c) 1 decametre = 10 metres
(d) 1 decimetre = $\dfrac{1}{10}$ or 0.1 metres
(e) 1 centimetre = $\dfrac{1}{100}$ or 0.01 metres
(f) 1 millimetre = $\dfrac{1}{1000}$ or 0.001 metres
For Mass or Weight:
(a) 10 milligrams = 1 centigram
(b) 10 centigrams = 1 decigram
(c) 10 decigrams = 1 gram
(d) 10 grams = 1 decagram
(e) 10 decagrams = 1 hectogram
(f) 10 hectograms = 1 kilogram
Relationship between measures of Mass or Weight:
(a) 1 kilogram = 1000 grams
(b) 1 gram = 100 centigrams
(c) 1 gram = 1000 milligrams
(d) 1 centigram - 10 milligrams
More Relationship between measures of Mass or Weight:
(a) 1 kilogram = 1000 grams
(b) 1 hectogram = 100 grams
(c) 1 decagram = 10 grams
(d) 1 decigram = $\dfrac{1}{10}$ or 0.1 grams
(e) 1 centigram = $\dfrac{1}{100}$ or 0.01 grams
(f) 1 milligram = $\dfrac{1}{1000}$ or 0.001 grams
For Capacity or Litre:
(a) 10 millilitres = 1 centilitre
(b) 10 centilitres = 1 decilitre
(c) 10 decilitres = 1 litre
(d) 10 litres = 1 decalitre
(e) 10 decalitres = 1 hectolitre
(f) 10 hectolitres = 1 kilolitre
Relationship between measures of Capacity or Litre:
(a) 1 kilolitre = 1000 litres
(b) 1 litre = 100 centilitres
(c) 1 litre = 1000 millilitres
(d) 1 centilitre - 10 millilitres
More Relationship between measures of Capacity or Litre:
(a) 1 kilolitre = 1000 litres
(b) 1 hectolitre = 100 litres
(c) 1 decalitre = 10 litres
(d) 1 decilitre = $\dfrac{1}{10}$ or 0.1 litres
(e) 1 centilitre = $\dfrac{1}{100}$ or 0.01 litres
(f) 1 millilitre = $\dfrac{1}{1000}$ or 0.001 litres
Conversion of unit of measurement:
Under the metric system, conversion of units is simple. To convert a given unit into a higher unit, we divide by 10, 100 or 1000. To convert a given unit into some smaller unit, we multiply it by 10, 100 or 1000.
Converting smaller to higher unit:
Eg. Convert 5864 centimetres into metres.
Solution: we know that 1 metre = 100 centimetres
$\therefore \dfrac{5864}{100}$ = 58.64 metres
Eg. Convert 5864 millimetres into metres.
Solution: we know that 1 metre = 1000 millimetres
$\therefore \dfrac{5864}{1000}$ = 5.864 metres
Eg. Convert 25 grams into kilograms.
Solution: we know that 1 kilogram = 1000 grams
$\therefore \dfrac{25}{1000}$ = 0.025 kilograms
Eg. Convert 50 litres into hectolitres.
Solution: we know that 1 hectolitre = 100 litres
$\therefore \dfrac{50}{1000}$ = 0.50 kilolitres
Converting higher to smaller unit:
Eg. Convert 50 grams into centigrams.
Solution: we know that 1 gram = 100 centigrams
$\therefore$ 50 $\times$ 100 = 5,000 centigrams
Eg. Convert 4 kilometres into metres.
Solution: we know that 1 kilometres = 1000 metres
$\therefore$ 4 $\times$ 1000 = 4,000 metres
Eg. Convert 30 litres into millilitres.
Solution: we know that 1 litre = 1000 millilitres
$\therefore$ 30 $\times$ 1000 = 30,000 millilitres
Under unit conversion, the decimal point is suitably shifted. When dividing, the decimal point is shifted towards the left. In multiplication, the decimal point is shifted towards the right.
Eg. Convert 3.4876 metres into decimetres, centimetres and millimetres.
Solution: we know that 1 metre = 10 decimetres
$\therefore \dfrac{34876}{10000}\times$ 10 = $\dfrac{3487}{1000}$ = 34.876 decimetres
we know that 1 metre = 100 centimetres
$\therefore \dfrac{34876}{10000}\times$ 100 = $\dfrac{3487}{100}$ = 348.76 centimetres
we know that 1 metre = 1000 millimetres
$\therefore \dfrac{34876}{10000}\times$ 1000 = $\dfrac{3487}{10}$ = 3487.6 millimetres
Eg. Convert 56.65 grams into decagrams, hectograms and kilograms.
Solution: we know that 10 grams = 1 decagram
$\therefore \dfrac{5665}{100 \times 10}$ = $\dfrac{5665}{1000}$ = 5.665 decagrams.
we know that 100 grams = 1 hectogram
$\therefore \dfrac{5665}{100 \times 100}$ = $\dfrac{5665}{10000}$ = 0.5665 hectograms.
we know that 1000 grams = 1 kilogram
$\therefore \dfrac{5665}{100 \times 1000}$ = $\dfrac{5665}{100000}$ = 0.05665 kilograms.
Some more examples:
Eg. Express 378 metres as decametre and metre.
Solution: $\therefore$ 378 metres = $\dfrac{370}{10}$ + 8 = 37 decametre and 8 metres.
Eg. Express 4235 grams as kilogram, hectogram, decagram and gram.
Solution: $\therefore$ 4235 grams = $\dfrac{4000}{1000}$ + $\dfrac{200}{100}$ + $\dfrac{30}{10}$ + 5
$\therefore$ 4 kilogram 2 hectogram 3 decagram and 5 grams.
Eg. Express 5 litres, 8 decilitres, 2 centilitres and 3 millilitres into millilitres.
$\therefore$ (5 $\times$ 1000) + (8 $\times$ 100) + (2 $\times$ 10) + (3 $\times$ 1)
$\therefore$ 5823 millimetres.
What is Estimation?
It is the process to make a fair guess. It provides a rough idea instead of an exact one.
Eg. 83 is about 80 and 98 is about 100. The guess result is 180 while the exact result is 181. The existing difference of 1 expresses a minute deviation. "Approximately" and "About" are the two most often used terms in Estimation. it is usually done by rounding off a given number to nearest 10, 100 or 1000. in case the given number is a middle one (5) then it is rounded to the nearest bigger number.
Eg. 125 is about 100
$\therefore$ 25 is about 30
$\therefore$ 175 is about 200
Question. If it takes 2 steps for a man to cover 2 meters then in how many steps will he be able to cover a distance of 1.5 kms.
Solution:
$\Rightarrow$ 1 km = 1000 meters
$\Rightarrow$ 1.5 kms = 1500 meters
$\Rightarrow$ Given, steps taken to cover 1 meter = $2$ steps
$\Rightarrow$ Steps taken to cover 100 meter = $2 \times 100 = 200$ steps
$\Rightarrow$ Steps taken to cover 1000 meter = $2 \times 1000 = 2000$ steps
$\therefore$ Steps taken to cover 1500 meter = $2 \times 1500 = 3000 $ steps Answer