Textbook: Decimal Fractions | Mathematics Class 6 (Maharashtra Board) PDF Download

 Page 1


29
Decimal Fractions : Addition and Subtraction 
 Nandu went to a shop to buy a pen, notebook, eraser and paintbox. The shopkeeper 
told him the prices. A pen costs four and a half rupees, an eraser one and a half, a notebook 
six and a half and a paintbox twenty- five rupees and fifty paise. Nandu bought one of each 
article. Prepare his bill. 
If Nandu gave a 100 rupee note, how much money does he get back?
100 -  = 
Nandu will get ................ rupees back.
 While solving problems with the units rupees- paise, metres- centimetres, we have used 
fractions with up to two decimal places. When solving problems with the units kilogram- gram, 
kilometre- metre, litre- millilitre, we have to use fractions with up to three decimal places.
Example : Reshma bought some vegetables. They included three- quarter kilo potatoes, 
one kilo onions, half a kilo cabbage and a quarter kilo tomatoes. What is the 
total weight of the vegetables in her bag?
We know : 1 kg  = 1000 g, half kg = 500 g, 
three- quarter kg = 750 g, quarter kg = 250 g
5
Decimal Fractions
 Ashay Vastu Bhandar
 Nandu
 S No.
S No 87 Date: 11.1.16
 Details
 Qty
 Amount
 1 Pen 1 4.50
 Total
Let’s recall.
Let’s learn.
Page 2


29
Decimal Fractions : Addition and Subtraction 
 Nandu went to a shop to buy a pen, notebook, eraser and paintbox. The shopkeeper 
told him the prices. A pen costs four and a half rupees, an eraser one and a half, a notebook 
six and a half and a paintbox twenty- five rupees and fifty paise. Nandu bought one of each 
article. Prepare his bill. 
If Nandu gave a 100 rupee note, how much money does he get back?
100 -  = 
Nandu will get ................ rupees back.
 While solving problems with the units rupees- paise, metres- centimetres, we have used 
fractions with up to two decimal places. When solving problems with the units kilogram- gram, 
kilometre- metre, litre- millilitre, we have to use fractions with up to three decimal places.
Example : Reshma bought some vegetables. They included three- quarter kilo potatoes, 
one kilo onions, half a kilo cabbage and a quarter kilo tomatoes. What is the 
total weight of the vegetables in her bag?
We know : 1 kg  = 1000 g, half kg = 500 g, 
three- quarter kg = 750 g, quarter kg = 250 g
5
Decimal Fractions
 Ashay Vastu Bhandar
 Nandu
 S No.
S No 87 Date: 11.1.16
 Details
 Qty
 Amount
 1 Pen 1 4.50
 Total
Let’s recall.
Let’s learn.
30
 Now to find out the total weight of the vegetables, let us add using both units, kilograms 
and grams, in turn. 
        
  Note the similarity between the addition    of 
integers and the addition of decimal fractions.
 Total weight of vegetables is 2500 g, that is 
2500
1000
 kg, that is 2.500 kg. 
 We know that, 2.500 = 2.50 = 2.5
 The weight of vegetables in Reshma’s bag is 2.5 kg.   
   
 Take a pen and notebook with you when you go to the market with your parents. Note 
the weight of every vegetable your mother buys. Find out the total weight of those vegetables.
1. In the table below, write the place value of each of the digits in the number 378.025.
 Place Hundreds  Tens Units Tenths Hundredths Thousandths
100 10 1
1
10
1
100
1
1000
Digit 3 7 8 0 2 5
Place value 300
0
10
 = 0
5
1000
 = 0.005
2. Solve.
 (1) 905.5 + 27.197 (2) 39 + 700.65 (3) 40 + 27.7 + 2.451
3. Subtract.
 (1) 85.96 - 2.345  (2) 632.24 - 97.45 (3) 200.005 - 17.186 
Potatoes   0.750 kg
Onions +  1.000 kg 
Cabbage  +  0.500 kg 
Tomatoes   +       0.250 kg 
Total weight      2.500 kg 
Potatoes     750 g
Onions  +  1000 g 
Cabbage  +  500 g 
Tomatoes   + 250 g 
Total weight    2500  
grams 
Practice Set 14
 
My friend, Maths : At the market, in the shop.
Page 3


29
Decimal Fractions : Addition and Subtraction 
 Nandu went to a shop to buy a pen, notebook, eraser and paintbox. The shopkeeper 
told him the prices. A pen costs four and a half rupees, an eraser one and a half, a notebook 
six and a half and a paintbox twenty- five rupees and fifty paise. Nandu bought one of each 
article. Prepare his bill. 
If Nandu gave a 100 rupee note, how much money does he get back?
100 -  = 
Nandu will get ................ rupees back.
 While solving problems with the units rupees- paise, metres- centimetres, we have used 
fractions with up to two decimal places. When solving problems with the units kilogram- gram, 
kilometre- metre, litre- millilitre, we have to use fractions with up to three decimal places.
Example : Reshma bought some vegetables. They included three- quarter kilo potatoes, 
one kilo onions, half a kilo cabbage and a quarter kilo tomatoes. What is the 
total weight of the vegetables in her bag?
We know : 1 kg  = 1000 g, half kg = 500 g, 
three- quarter kg = 750 g, quarter kg = 250 g
5
Decimal Fractions
 Ashay Vastu Bhandar
 Nandu
 S No.
S No 87 Date: 11.1.16
 Details
 Qty
 Amount
 1 Pen 1 4.50
 Total
Let’s recall.
Let’s learn.
30
 Now to find out the total weight of the vegetables, let us add using both units, kilograms 
and grams, in turn. 
        
  Note the similarity between the addition    of 
integers and the addition of decimal fractions.
 Total weight of vegetables is 2500 g, that is 
2500
1000
 kg, that is 2.500 kg. 
 We know that, 2.500 = 2.50 = 2.5
 The weight of vegetables in Reshma’s bag is 2.5 kg.   
   
 Take a pen and notebook with you when you go to the market with your parents. Note 
the weight of every vegetable your mother buys. Find out the total weight of those vegetables.
1. In the table below, write the place value of each of the digits in the number 378.025.
 Place Hundreds  Tens Units Tenths Hundredths Thousandths
100 10 1
1
10
1
100
1
1000
Digit 3 7 8 0 2 5
Place value 300
0
10
 = 0
5
1000
 = 0.005
2. Solve.
 (1) 905.5 + 27.197 (2) 39 + 700.65 (3) 40 + 27.7 + 2.451
3. Subtract.
 (1) 85.96 - 2.345  (2) 632.24 - 97.45 (3) 200.005 - 17.186 
Potatoes   0.750 kg
Onions +  1.000 kg 
Cabbage  +  0.500 kg 
Tomatoes   +       0.250 kg 
Total weight      2.500 kg 
Potatoes     750 g
Onions  +  1000 g 
Cabbage  +  500 g 
Tomatoes   + 250 g 
Total weight    2500  
grams 
Practice Set 14
 
My friend, Maths : At the market, in the shop.
31
4. Avinash travelled 42 km 365 m by bus, 12 km 460 m by car and walked 640 m. How
many kilometres did he travel altogether? (Write your answer in decimal fractions.)
5. Ayesha bought 1.80 m of cloth for her salwaar and 2.25 m for her kurta. If the cloth
costs 120 rupees per metre, how much must she pay the shopkeeper?
6. Sujata bought a watermelon weighing 4.25 kg and gave 1 kg 750g to the children in her
neighbourhood. How much of it does she have left?
7. Anita was driving at a speed of 85.6 km per hour. The road had a speed limit of
55 km per hour. By how much should she reduce her speed to be within the
speed limit?
Showing Decimal Fractions on the Number Line
Example : Observe how the numbers 0.7 and 6.5 are marked on the number line. 
In the same way, show the following numbers on the number line.
(1) 3.5 (2) 0.8 (3) 1.9 (4) 4.2 (5) 2.7
Converting a Common Fraction into a Decimal Fraction
 You know that if the denominator of a common fraction is 10 or 100,  it can be written 
as a decimal fraction. 
Can you recall how to convert the fractions 
1
2
, 
1
4
, 
2
5
 into decimal fractions?
 A fraction whose denominator is 1000 can also be written as a decimal fraction. Let us 
see how.
If the denominator of a common fraction is 10, 100, 1000, then - 
(1)	 If there are more digits in the numerator than zeros in the denominator, then count as
many digits from the right as the number of zeros, and place the decimal point before
those digits.
Examples  (1) 
723
10
 = 72.3 (2) 
51250
100
 = 512.50  (3) 
5138
1000
 = 5.138
6.5
0.7
Let’s recall.
Let’s learn.
Page 4


29
Decimal Fractions : Addition and Subtraction 
 Nandu went to a shop to buy a pen, notebook, eraser and paintbox. The shopkeeper 
told him the prices. A pen costs four and a half rupees, an eraser one and a half, a notebook 
six and a half and a paintbox twenty- five rupees and fifty paise. Nandu bought one of each 
article. Prepare his bill. 
If Nandu gave a 100 rupee note, how much money does he get back?
100 -  = 
Nandu will get ................ rupees back.
 While solving problems with the units rupees- paise, metres- centimetres, we have used 
fractions with up to two decimal places. When solving problems with the units kilogram- gram, 
kilometre- metre, litre- millilitre, we have to use fractions with up to three decimal places.
Example : Reshma bought some vegetables. They included three- quarter kilo potatoes, 
one kilo onions, half a kilo cabbage and a quarter kilo tomatoes. What is the 
total weight of the vegetables in her bag?
We know : 1 kg  = 1000 g, half kg = 500 g, 
three- quarter kg = 750 g, quarter kg = 250 g
5
Decimal Fractions
 Ashay Vastu Bhandar
 Nandu
 S No.
S No 87 Date: 11.1.16
 Details
 Qty
 Amount
 1 Pen 1 4.50
 Total
Let’s recall.
Let’s learn.
30
 Now to find out the total weight of the vegetables, let us add using both units, kilograms 
and grams, in turn. 
        
  Note the similarity between the addition    of 
integers and the addition of decimal fractions.
 Total weight of vegetables is 2500 g, that is 
2500
1000
 kg, that is 2.500 kg. 
 We know that, 2.500 = 2.50 = 2.5
 The weight of vegetables in Reshma’s bag is 2.5 kg.   
   
 Take a pen and notebook with you when you go to the market with your parents. Note 
the weight of every vegetable your mother buys. Find out the total weight of those vegetables.
1. In the table below, write the place value of each of the digits in the number 378.025.
 Place Hundreds  Tens Units Tenths Hundredths Thousandths
100 10 1
1
10
1
100
1
1000
Digit 3 7 8 0 2 5
Place value 300
0
10
 = 0
5
1000
 = 0.005
2. Solve.
 (1) 905.5 + 27.197 (2) 39 + 700.65 (3) 40 + 27.7 + 2.451
3. Subtract.
 (1) 85.96 - 2.345  (2) 632.24 - 97.45 (3) 200.005 - 17.186 
Potatoes   0.750 kg
Onions +  1.000 kg 
Cabbage  +  0.500 kg 
Tomatoes   +       0.250 kg 
Total weight      2.500 kg 
Potatoes     750 g
Onions  +  1000 g 
Cabbage  +  500 g 
Tomatoes   + 250 g 
Total weight    2500  
grams 
Practice Set 14
 
My friend, Maths : At the market, in the shop.
31
4. Avinash travelled 42 km 365 m by bus, 12 km 460 m by car and walked 640 m. How
many kilometres did he travel altogether? (Write your answer in decimal fractions.)
5. Ayesha bought 1.80 m of cloth for her salwaar and 2.25 m for her kurta. If the cloth
costs 120 rupees per metre, how much must she pay the shopkeeper?
6. Sujata bought a watermelon weighing 4.25 kg and gave 1 kg 750g to the children in her
neighbourhood. How much of it does she have left?
7. Anita was driving at a speed of 85.6 km per hour. The road had a speed limit of
55 km per hour. By how much should she reduce her speed to be within the
speed limit?
Showing Decimal Fractions on the Number Line
Example : Observe how the numbers 0.7 and 6.5 are marked on the number line. 
In the same way, show the following numbers on the number line.
(1) 3.5 (2) 0.8 (3) 1.9 (4) 4.2 (5) 2.7
Converting a Common Fraction into a Decimal Fraction
 You know that if the denominator of a common fraction is 10 or 100,  it can be written 
as a decimal fraction. 
Can you recall how to convert the fractions 
1
2
, 
1
4
, 
2
5
 into decimal fractions?
 A fraction whose denominator is 1000 can also be written as a decimal fraction. Let us 
see how.
If the denominator of a common fraction is 10, 100, 1000, then - 
(1)	 If there are more digits in the numerator than zeros in the denominator, then count as
many digits from the right as the number of zeros, and place the decimal point before
those digits.
Examples  (1) 
723
10
 = 72.3 (2) 
51250
100
 = 512.50  (3) 
5138
1000
 = 5.138
6.5
0.7
Let’s recall.
Let’s learn.
32
(2)	 If there are as many digits in the numerator as zeros in the denominator, place the
decimal point before the number in the numerator and a zero in the integers’ place.
Examples  (1) 
7
10
 = 0.7 (2) 
54
100
= 0.54  (3) 
725
1000
 = 0.725
(3)	 If there are fewer digits in the numerator than the zeros in the denominator, place zeros
before the digits in the numerator to make the total number of digits equal to the
number of zeros in the denominator. Place a decimal point before them and a zero in
the integers’ place.
Examples  (1) 
8
100
 = 
08
100
 = 0.08        (2) 
8
1000
 = 
008
1000
 = 0.008
Converting a Decimal Fraction into a Common Fraction 
(1) 26.4 = 
264
10
(2) 0.04 = 
4
100
(3) 19.315 = 
19315
1000
This is how we convert a decimal fraction into a common fraction. In the numerator, 
we write the number we get by ignoring the decimal point. In the denominator, we 
write 1 followed by as many zeros as there are decimal places in the given number.
1. Write the proper number in the empty boxes.
 (1) 
3
5
 = 
3
5
×
×
= 
10
 = (2) 
25
8
 = 
25×
8×125
 = 
1000
 = 3.125
 (3) 
21
2
= 
21
2
×
×
 
=
 
10
=
  (4) 
22
40
 = 
11
20
 = 
11
20 5
×
×
= 
100
 =
2. Convert the common fractions into decimal fractions.
 (1) 
3
4
 (2) 
4
5
 (3) 
9
8
 (4) 
17
20
 (5) 
36
40
 (6) 
7
25
 (7) 
19
200
3. Convert the decimal fractions into common fractions.
(1) 27.5 (2) 0.007 (3) 90.8 (4) 39.15 (5) 3.12 (6) 70.400
Practice Set 15
Let’s learn.
Now I know -
Page 5


29
Decimal Fractions : Addition and Subtraction 
 Nandu went to a shop to buy a pen, notebook, eraser and paintbox. The shopkeeper 
told him the prices. A pen costs four and a half rupees, an eraser one and a half, a notebook 
six and a half and a paintbox twenty- five rupees and fifty paise. Nandu bought one of each 
article. Prepare his bill. 
If Nandu gave a 100 rupee note, how much money does he get back?
100 -  = 
Nandu will get ................ rupees back.
 While solving problems with the units rupees- paise, metres- centimetres, we have used 
fractions with up to two decimal places. When solving problems with the units kilogram- gram, 
kilometre- metre, litre- millilitre, we have to use fractions with up to three decimal places.
Example : Reshma bought some vegetables. They included three- quarter kilo potatoes, 
one kilo onions, half a kilo cabbage and a quarter kilo tomatoes. What is the 
total weight of the vegetables in her bag?
We know : 1 kg  = 1000 g, half kg = 500 g, 
three- quarter kg = 750 g, quarter kg = 250 g
5
Decimal Fractions
 Ashay Vastu Bhandar
 Nandu
 S No.
S No 87 Date: 11.1.16
 Details
 Qty
 Amount
 1 Pen 1 4.50
 Total
Let’s recall.
Let’s learn.
30
 Now to find out the total weight of the vegetables, let us add using both units, kilograms 
and grams, in turn. 
        
  Note the similarity between the addition    of 
integers and the addition of decimal fractions.
 Total weight of vegetables is 2500 g, that is 
2500
1000
 kg, that is 2.500 kg. 
 We know that, 2.500 = 2.50 = 2.5
 The weight of vegetables in Reshma’s bag is 2.5 kg.   
   
 Take a pen and notebook with you when you go to the market with your parents. Note 
the weight of every vegetable your mother buys. Find out the total weight of those vegetables.
1. In the table below, write the place value of each of the digits in the number 378.025.
 Place Hundreds  Tens Units Tenths Hundredths Thousandths
100 10 1
1
10
1
100
1
1000
Digit 3 7 8 0 2 5
Place value 300
0
10
 = 0
5
1000
 = 0.005
2. Solve.
 (1) 905.5 + 27.197 (2) 39 + 700.65 (3) 40 + 27.7 + 2.451
3. Subtract.
 (1) 85.96 - 2.345  (2) 632.24 - 97.45 (3) 200.005 - 17.186 
Potatoes   0.750 kg
Onions +  1.000 kg 
Cabbage  +  0.500 kg 
Tomatoes   +       0.250 kg 
Total weight      2.500 kg 
Potatoes     750 g
Onions  +  1000 g 
Cabbage  +  500 g 
Tomatoes   + 250 g 
Total weight    2500  
grams 
Practice Set 14
 
My friend, Maths : At the market, in the shop.
31
4. Avinash travelled 42 km 365 m by bus, 12 km 460 m by car and walked 640 m. How
many kilometres did he travel altogether? (Write your answer in decimal fractions.)
5. Ayesha bought 1.80 m of cloth for her salwaar and 2.25 m for her kurta. If the cloth
costs 120 rupees per metre, how much must she pay the shopkeeper?
6. Sujata bought a watermelon weighing 4.25 kg and gave 1 kg 750g to the children in her
neighbourhood. How much of it does she have left?
7. Anita was driving at a speed of 85.6 km per hour. The road had a speed limit of
55 km per hour. By how much should she reduce her speed to be within the
speed limit?
Showing Decimal Fractions on the Number Line
Example : Observe how the numbers 0.7 and 6.5 are marked on the number line. 
In the same way, show the following numbers on the number line.
(1) 3.5 (2) 0.8 (3) 1.9 (4) 4.2 (5) 2.7
Converting a Common Fraction into a Decimal Fraction
 You know that if the denominator of a common fraction is 10 or 100,  it can be written 
as a decimal fraction. 
Can you recall how to convert the fractions 
1
2
, 
1
4
, 
2
5
 into decimal fractions?
 A fraction whose denominator is 1000 can also be written as a decimal fraction. Let us 
see how.
If the denominator of a common fraction is 10, 100, 1000, then - 
(1)	 If there are more digits in the numerator than zeros in the denominator, then count as
many digits from the right as the number of zeros, and place the decimal point before
those digits.
Examples  (1) 
723
10
 = 72.3 (2) 
51250
100
 = 512.50  (3) 
5138
1000
 = 5.138
6.5
0.7
Let’s recall.
Let’s learn.
32
(2)	 If there are as many digits in the numerator as zeros in the denominator, place the
decimal point before the number in the numerator and a zero in the integers’ place.
Examples  (1) 
7
10
 = 0.7 (2) 
54
100
= 0.54  (3) 
725
1000
 = 0.725
(3)	 If there are fewer digits in the numerator than the zeros in the denominator, place zeros
before the digits in the numerator to make the total number of digits equal to the
number of zeros in the denominator. Place a decimal point before them and a zero in
the integers’ place.
Examples  (1) 
8
100
 = 
08
100
 = 0.08        (2) 
8
1000
 = 
008
1000
 = 0.008
Converting a Decimal Fraction into a Common Fraction 
(1) 26.4 = 
264
10
(2) 0.04 = 
4
100
(3) 19.315 = 
19315
1000
This is how we convert a decimal fraction into a common fraction. In the numerator, 
we write the number we get by ignoring the decimal point. In the denominator, we 
write 1 followed by as many zeros as there are decimal places in the given number.
1. Write the proper number in the empty boxes.
 (1) 
3
5
 = 
3
5
×
×
= 
10
 = (2) 
25
8
 = 
25×
8×125
 = 
1000
 = 3.125
 (3) 
21
2
= 
21
2
×
×
 
=
 
10
=
  (4) 
22
40
 = 
11
20
 = 
11
20 5
×
×
= 
100
 =
2. Convert the common fractions into decimal fractions.
 (1) 
3
4
 (2) 
4
5
 (3) 
9
8
 (4) 
17
20
 (5) 
36
40
 (6) 
7
25
 (7) 
19
200
3. Convert the decimal fractions into common fractions.
(1) 27.5 (2) 0.007 (3) 90.8 (4) 39.15 (5) 3.12 (6) 70.400
Practice Set 15
Let’s learn.
Now I know -
33
	 The rate of petrol is ` 62.32 per litre. Seema 
wants to fill two and a half litres of petrol in 
her scooter. How many rupees will she have 
to pay?
	 Which operation is required?
Multiplication of Decimal Fractions
Example 1. Multiply 4.3 × 5. 
   Method I Method II                   Method III
 
Example 2.
   Method I  
   62.32 × 2.5 = ?
   62.32 × 2.5 = 
6232
100
 × 
25
10
 
  = 
155800
1000
   
  = 155.800 
 Seema will have to pay `155.80
  
1. If, 317 × 45 = 14265, then 3.17 × 4.5 = ?
2. If, 503 × 217 = 109151, then 5.03 × 2.17 = ? 
3. Multiply.
 (1) 2.7 × 1.4  (2) 6.17 × 3.9 (3) 0.57 × 2 (4) 5.04 × 0.7
Method II
?? First, multiply ignoring the decimal point. 
?? Then, in the product, starting from the units 
place, we count as many places as the total 
decimal places in the multiplicand and 
multiplier, and place the decimal point before 
them.
 6232 62.32
 
×
 25 
×
 2.5
 155800 155.800
4.3 × 5 = 
43
10
 × 
5
1
   = 
43 5
10 1
×
×
   = 
215
10
4.3 × 5 = 21.5
× 4
3
10
5 20
15
10
4.3 × 5 = 20 + 1.5 = 21.5
 43
 
×
 5
 215
 4.3
 
×
 5
 21.5
20 1.5
Practice Set 16
Let’s learn.