Decimal Fractions

decimal fractions

Step by Step solutions of RS Aggarwal ICSE Class-6 Maths chapter 5- Decimal Fractions by Goyal Brothers Prakashan is provided.

Table of Contents

Exercise: 5-E

Q1: Rajan purchased a geometry box for ₹136.75, a colour box for ₹48.80 and a register for ₹64.50. What amount did he pay to the shopkeeper?

Step 1: Add the prices of all three items:

 136.75
+ 48.80
+ 64.50
--------
 250.05

Answer: ₹250.05


Q2: Sakshi bought 3 m 28 cm cloth for her shirt and 2 m 7 cm for her trousers. What is the total length of cloth bought by her?

Step 1: Add the lengths separately:

Metres     Centimetres
   3            28
+  2            07
---------------------
   5            35

Step 2: No need to convert cm since total is less than 100.
Answer: 5 metres 35 centimetres


Q3: A bag contains 95 kg 80 g of rice and the mass Of the empty bag is 860 g. What is the weight of the bag filled with rice?

Step 1: Separate into kilograms and grams:
Rice: 95 kg 80 g
Empty bag: 0 kg 860 g
Step 2: Add kilograms and grams separately:

Kilograms    Grams
   95          80
+   0         860
------------------
   95         940

Step 3: Since grams < 1000, no need to convert further.
Answer: 95 kg 940 g


Q4: Distance between Delhi and Meerut is 85 km 850m and the distance between Meerut and Muzaffarnagar is 56 km 85 m. What is the distance between Delhi and Muzaffarnagar?

Step 1: Write distances in km and m columns.
Delhi → Meerut = 85 km 850 m
Meerut → Muzaffarnagar = 56 km 85 m
Step 2: Add kilometers and meters separately:

Kilometers   Meters
   85         850
+  56          85
-------------------
  141         935

Step 3: Since 935 m < 1000, no conversion needed.
Answer: 141 km 935 m


Q5: Divya purchased a book worth ₹256.85 and a set of note-books worth ₹546.70. She gave a ₹2000 note to the shopkeeper. How much money did she get back?

Step 1: Add the cost of the book and the set of note-books:

 256.85
+546.70
--------
 803.55

Step 2: Subtract total amount from ₹20000:

2000.00
-803.55
---------
1196.45

Answer: ₹1196.45


Q6: The weight of a gas cylinder filled with gas is 32 kg 200 g. If the weight of the gas contained in it is 17 kg 80 g, find the weight of the empty cylinder.

Step 1: Total weight (filled): 32 kg 200 g
Weight of gas: 17 kg 80 g
We subtract to get the empty weight.
Step 2: Subtract kilograms and grams separately:

Kilograms    Grams
   32         200
-  17          80
-------------------
   15         120

Answer: 15 kg 120 g


Q7: Stuti went the market with ₹3000 in cash. Out of this money, she purchased one frock, one toy and one bag costing ₹675.85, ₹318 and ₹1972.75 respectively. How much money is left with her?

Step 1: Add the prices of the frock, toy, and bag:

  675.85
+ 318.00
+1972.75
---------
 2966.60

Step 2: Subtract the total expense from ₹3000:

 3000.00
-2966.60
---------
  33.40

Answer: ₹33.40


Q8: The total weight of a bag containing 25 kg 750 g of potatoes and 18 kg 80 g of melon is 44 kg 200 g. How much is the weight of the empty bag?

Step 1: Add weight of potatoes and melon:

Kilograms    Grams
   25         750
+  18          80
-------------------
   43         830

Step 2: Total weight of filled bag = 44 kg 200 g
Now subtract the content weight from total:

Kilograms    Grams
   44         200
-  43         830

Since 200 g is less than 830 g, borrow 1 kg = 1000 g:

Kilograms    Grams
   43        1200   ← (borrowed 1 kg)
-  43         830
-------------------
    0         370

Answer: 370 g


Q9: If the school bags of Divya and Rahul weigh 8 kg 60 g and 6 kg 275 g respectively, whose bag is heavier and by how much?

Step 1: We are given:
Divya’s bag = 8 kg 60 g
Rahul’s bag = 6 kg 275 g
Step 2: Compare the weights.
Clearly, Divya’s bag is heavier.
Step 3: Subtract Rahul’s bag weight from Divya’s to find the difference:
Since 60 g < 275 g, borrow 1 kg = 1000 g
So, 8 kg 60 g becomes → 7 kg 1060 g

Kilograms    Grams
    7         1060
 -  6          275
--------------------
    1          785

Answer: Divya’s bag is heavier by 1 kg 785 g


Q10: The distance between Naman’s office and his house is 19 km. He covers 14 km 65m by scooter, 3 km 75 m by bus and the rest on foot. How much distance does he cover by walking?

Step 1: Add distance by scooter and by bus:

Kilometres    Metres
    14          65
+    3          75
----------------------
    17         140

Step 2: Total distance = 19 km = 19 km 0 m
Now subtract 17 km 140 m from 19 km 0 m:
Since 0 m < 140 m, borrow 1 km = 1000 m:
19 km 0 m → 18 km 1000 m

Kilometres    Metres
    18         1000
 -  17          140
----------------------
     1          860

Answer: Naman covers 1 km 860 m by walking


Q11: There was an electric wire of length 100 m. Out of it three pieces of length 26 m 85 cm, 3 m 18 cm, 18 m 70 cm were cut off. What is the length of the remaining wire?

Step 1: Add the lengths of the three pieces cut off:

Metres     Centimetres
  26           85
+  3           18
+ 18           70
---------------------
  47          173

Step 2: Since 173 cm = 1 m 73 cm, convert:

 47 m 173 cm = 48 m 73 cm

Step 3: Subtract the total cut length from 100 m:

Metres     Centimetres
 100           00
- 48           73
---------------------
Since 00 < 73, borrow 1 m = 100 cm:
  99         100
- 48          73
---------------------
  51          27

Answer: The remaining length of the wire is 51 m 27 cm


Q12: A bag contained 98 kg 300 g of wheat. There was a consumption of 36 kg 450 g, 28 kg 360 g and 32 kg 880 g during three months. How much wheat remains in the bag?

Step 1: Add the consumed quantities:

Kilograms    Grams
   36         450
+  28         360
+  32         880
---------------------
   96        1690

Step 2: Convert 1690 g = 1 kg 690 g
So total consumption becomes:

96 kg 1690 g = 97 kg 690 g

Step 3: Subtract from the original amount of wheat (98 kg 300 g):

Since 300 g < 690 g, borrow 1 kg = 1000 g:
 98 kg 300 g → 97 kg 1300 g

Now subtract:
Kilograms    Grams
   97         1300
 - 97          690
---------------------
    0          610

Answer: 610 g of wheat remains in the bag


Q13: Out of 260 litres of milk, a milkman sold 36 l 500 ml, 75 l 750 ml, 68 l 400 ml and 42 l 850 ml. How much milk is left with him?

Step 1: Add the sold quantities:

Litres     Millilitres
  36           500
+ 75           750
+ 68           400
+ 42           850
-----------------------
 221          2500

Step 2: Convert 2500 ml = 2 litres 500 ml
So,
221 l 2500 ml = 223 l 500 ml
Step 3: Subtract from total milk (260 l 0 ml):
Since 0 ml < 500 ml, borrow 1 litre = 1000 ml:
260 l 0 ml → 259 l 1000 ml
Now subtract:

 259 l 1000 ml
-223 l  500 ml
-------------------
  36 l  500 ml

Answer: 36 litres 500 millilitres of milk is left


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