Ex-7.1, Decimals, Class 6, Maths RD Sharma Solutions | RD Sharma Solutions for Class 6 Mathematics PDF Download

Page No 7.14:

Question 1: Write each of the following as decimals:

(i) Five hundred twenty five and forty hundredths.

(ii) Twelve and thirty five thousandths.

(iii) Fifteen and seventeen thousandths.

(iv) Eighty eight and forty eight-hundredths.
ANSWER:

Page No 7.15:

Question 2: Write each of the following as decimals:

ANSWER:

(i) We have 1 hundred, 3 tens, 7 ones and 5 hundredths.

Therefore, the decimal is137.05.

(ii) We have 2 tens, 9 ones and 4 hundredths.

Therefore, the decimal is 29.04.

Page No 7.15:

Question 3: Write each of the following as decimals:

ANSWER:

(i) We have 8 hundredths.

Therefore, the decimal is 0.08.

(ii) In its lowest form, the fraction is 310310.

We have 3 tenths.

Therefore, the decimal is 0.3.

(iii) We have eighteen thousandths.

Therefore, the decimal is 0.018.

Page No 7.15:

Question 4: Write each of the following as decimals:

ANSWER:

Page No 7.15:

Question 5: Write each of the following decimals as fractions. Reduce the fractions to lowest form:

(i) 0.04
(ii) 2.34
(iii) 0.342
(iv) 1.20
(v) 17.38

ANSWER:

(i) 0.04

  =0 + 0.04

  = 0 + 4 hundredths

(ii) 2.34

   = 2 + 0.34

   = 2 + 34 hundredths

(iii) 0.342

     = 0 + 342 thousandths

(iv) 1.20

    = 1 + 0.20

    = 1 + 20 hundredths

(v) 17.38

    = 17 + 0.38

    = 17 + 38 hundredths

Page No 7.15:

Question 6: Write each of the following as decimals:

ANSWER:
(i) Here, we have 2 tens, 9 ones, 4 tenths and 1 hundredths.

 Therefore, the decimal is 29.41.
(ii) Here, we have 3 tens, 4 tenths, 8 hundredths and 3 thousandths.

Therefore, the decimal is 30.483.
(iii) Here, we have 1 hundred, 3 tens, 7 ones and 5 hundredths.

Therefore, the decimal is 137.05.
(iv) Here, we have 7 tenths, 6 hundredths and 4 thousandths.

Therefore, the decimal is 0.764.
(v)  Here, we have 2 tens, 3 ones, 2 tenths and 6 thousandths.

Therefore, the decimal is 23.206.

(vi) Here, we have 7 hundreds, 2 tens , 5 ones and 9 hundredths.

Therefore, the decimal is 725.09.

Page No 7.19:

Question 1: Express the following fractions as decimals:

ANSWER:

Page No 7.19:

Question 2: Express the following decimals as fractions in the lowest form:

(i) 0.5

(ii) 2.5

(iii) 0.60

(iv) 0.18

(v) 5.25

(vi) 7.125

(vii) 15.004

(viii) 20.375

(ix) 600.75

(x) 59.48

ANSWER:

Page No 7.20:

Question 1: Fill in the blanks by using > or < to complete the following:

(i) 25.35....8.47

(ii) 20.695...20.93

(iii) 0.39...0.72

(iv) 0.109...0.83

(v) 0.236...0.201

(vi) 0.93...0.99

ANSWER:

(i) 25.35 > 8.47

 Here, the whole part 23 > 8.

(ii) 20.695 < 20.93

Here, the whole parts are equal. Hence, we should check the tenth parts. Now, 9 is greater than 6.

Therefore, 20 + 6/10 +9/100 +5/1000 < 20 + 9/10 + 3/100.

(iii) 0.39 < 0.72

Here, the whole parts are 0. Hence, we should check the tenth parts. Now, 3<7.

Therefore, 3/10 +9/100 < 7/10 + 2/100.

(iv) 0.109 < 0.83

Here, the whole parts are 0. Hence, we should check the tenth parts. Now, 1<8.

Therefore, 1/10 +9/1000 < 8/10 + 3/100.

(v) 0.236 > 0.201

Here, the whole parts are 0. Hence, we should check the tenth parts in the two numbers, which are again equal.

So, we should now check the hundredth digit, 3 > 0.

Therefore, 2/10 +3/100 +6/1000 > 2/10 +0/100 +1/1000.

(vi) 0.93 < 0.99

Here, the whole parts are 0. Hence, we should check the tenth parts, which are again equal.

So, we should now check the hundredth digit, 3< 9.

Therefore, 9/10 + 3/100 < 9/10+9/100.

Page No 7.20:

Question 2: Which is greater? Give reason for your answer?

(i) 1.008 or 1.800

(ii) 3.3 or 3.300

(iii) 5.64 or 5.603

(iv) 1.5 or 1.50

(v) 1.431 or 1.439

(vi) 0.5 or 0.05

ANSWER:

(i) 1.008 < 1.800

The whole parts are equal, and comparing the tenth parts, we have 0 < 8.

Therefore, 1+ 0/10 +8/1000 < 1+8/10.

(ii) 3.3 = 3.300

The whole parts and the tenth parts are both equal.

(iii) 5.64 > 5.603

The whole parts and the tenth parts are both equal. Comparing the hundredth parts, we have 4 > 0.

Therefore, 5+ 6/10 + 4/100 > 5 + 6/10 + 0/100 + 3/1000.

(iv) 1.5 = 1.50

The whole parts and the tenth parts are both equal.

(v) 1.431 < 1.439

The whole parts, the tenth parts and the hundredth parts are all equal. Comparing the thousandth parts, we have 1 < 9.

Therefore, 1+ 4/10 + 3/100 + 1/1000 < 1+4/10 + 3/100 + 9/1000.

(vi) 0.5  > 0.05

The whole parts are both 0. Comparing the tenth parts, we have 5 > 0.

Therefore, 5/10 > 0/10 +5/100.

Page No 7.24:

Question 1: Express as Rupee (Rs) using decimals:

(i) 15 paisa

(ii) 5 paisa

(iii) 350 paisa

(iv) 2 rupees 60 paisa

ANSWER:
(i) 15 paisa

We know that 100 paisa = Rs 1.

Therefore, 1 paisa = Rs 1/100.

15 paisa = 15/100 = Rs 0.15

(ii) 5 paisa

We know that 100 paisa = Rs 1.

Therefore, 1 paisa = Rs 1/100.

5 paisa = 5/100 = Rs 0.05

(iii) 350 paisa

We know that 100 paisa = Rs 1.

Therefore, 1 paisa = Rs 1/100.

350 paisa = 350/100 = Rs 3.50

(iv) 2 rupees 60 paisa

We know that 100 paisa = Rs 1.

Therefore, 1 paisa = Rs 1/100.

Page No 7.24:

Question 2: Express as metres (m) using decimals:

(i) 15 cm

(ii) 8 cm

(iii) 135 cm

(iv) 3m 65 cm

ANSWER:

(i) 15 cm

We know that 100 cm= 1 m.

Therefore, 1 cm = 1/100 m.

15 cm = 15*1/100 m = 15/100 = 0.15m

(ii) 8 cm

We know that 100 cm= 1 m.

Therefore, 1 cm = 1/100 m.

8 cm = 8/100= 0.08m

(iii) 135 cm

We know that 100 cm= 1 m.

Therefore, 1 cm = 1/100 m.

135 cm = 135/100 = 1.35 m

(iv) 3 m 65 cm

We know that 100 cm= 1 m.

Therefore, 1 cm = 1/100 m.

3m 65 cm = 3 + 65/100

= 3.65 m

Page No 7.24:

Question 3: Express as centimetre (cm) using decimals:

(i) 5 mm

(ii) 60 mm

(iii) 175 mm

(iv) 4cm 5 mm

ANSWER:

(i) 5 mm

We know that 10 mm = 1 cm.

Therefore, 1 mm = 1/10 cm.

5 mm = 5/10= 0.5 cm

(ii) 60 mm

We know that 10 mm = 1 cm.

Therefore, 1 mm = 1/10 cm.

60 mm = 60/10 = 6 cm

(iii) 175 mm

We know that 10 mm = 1 cm.

Therefore, 1 mm = 1/10 cm.

175 mm = 175/10 = 17.5 cm

(iv) 4 cm 5 mm

We know that 10 mm = 1 cm.

Therefore, 1 mm = 1/10 cm.

Page No 7.24:

Question 4: Express as kilometre (km) using decimals:

(i) 5 m

(ii) 55 m

(iii) 555 m

(iv) 5555 m

(v) 15 km 35 m

ANSWER:

(i) 5 m

We know that 1000 m = 1 km.

Therefore, 1 m = 1/1000 km = 0.001 km.

5 m = 5/1000 = 0.005 km

(ii) 55 m

We know that 1000 m = 1 km.

Therefore, 1 m = 1/1000 km = 0.001 km.

55 m = 55/1000 = 0.055 km

(iii) 555 m

We know that 1000 m = 1 km.

Therefore, 1 m = 1/1000 km = 0.001 km.

555 m = 555/1000 = 0.555 km

(iv) 5555 m

We know that 1000 m = 1 km.

Therefore, 1 m = 1/1000 km = 0.001 km.

5555 m = 5555/1000 = 5.555 km

(v) 15 km 35 m

We know that 1000 m = 1 km.

Therefore, 1 m = 1/1000 km = 0.001 km.

15 km 35 m = 15 + 35100015 + 351000

                   =15.035 km

Page No 7.24:

Question 5: Express as kilogram (kg) using decimals:

(i) 8 g

(ii) 150 g

(iii) 2750 g

(iv) 5 kg 750 g

(v) 36 kg 50 g

ANSWER:

(i) 8 g

We know that 1000 g = 1 kg.

Therefore, 1 g = 1/1000= 0.001 kg.

8 g = 8/1000= 0.008 kg

(ii) 150 g

We know that 1000 g = 1 kg.

Therefore, 1 g = 1/1000= 0.001 kg.

150 g = 150/1000 = 0.150 kg

(iii) 2750 g

We know that 1000 g = 1 kg.

Therefore, 1 g = 1/1000= 0.001 kg.

2750 g = 2.750 kg

(iv) 5 kg 750 g

We know that 1000 g = 1 kg.

Therefore, 1 g = 1/1000= 0.001 kg.

(v) 36 kg 50 g

We know that 1000 g = 1 kg.

Therefore, 1 g = 1/1000= 0.001 kg.

Page No 7.24:

Question 6: Express each of the following without using decimals:

(i) Rs 5.25

(ii) 8.354 kg

(iii) 3.5 cm

(iv) 3.05 km

(v) 7.54 m

(vi) 15.005 kg

(vii) 12.05 m

(viii) 0.2 cm

ANSWER:

(i) Rs 5.25

We know that 100 paisa = 1 rupee.

So, 1 paisa = 1/100 rupee.

Therefore, Rs 5.25 = 5 + 0.25

(ii) 8.354 kg

We know that 1000 g = 1 kg.

So, 1 g = 1/1000 kg.

Therefore, 8.354 = 8+ 0.354

(iii) 3.5 cm

We know that 10 mm = 1 cm.

So, 1 mm = 1/10 cm.

Therefore, 3.5= 3+ 0.5

= 3 cm and 5 mm
(iv) 3.05 km

We know that 1000 m = 1 km.

Therefore, 3.05 = 3+ .05

= 3+ 5/100 = 3+ 50/1000 km

= 3 km and 50 m
(v) 7.54 m

We know that 100 cm = 1 m.

Therefore, 7.54 = 7+ 0.54

= 7+ 54/100

= 7 m and 54 cm

(vi) 15.005 kg

We know that 1 kg = 1000 g.

Therefore, 15.005= 15 + 0.005

= 15+ 5/1000

= 15 kg and 5 g

(vii) 12.05 m

We know that 1 m = 100 cm.

Therefore, 12.05 = 12 +.05

= 12 + 5/100

= 12 m and 5 cm

(viii) 0.2 cm

We know that 1 cm = 10 mm.

Therefore, 0.2 = 2/10

= 2 mm

Page No 7.26:

Question 1: Choose the decimal (s) from the brackets which is (are) not equivalent to the given decimals:

(i) 0.8                    (0.80, 0.85, 0.800, 0.08)

(ii) 25.1                 (25.01, 25.10, 25.100, 25.001)

(iii) 45.05              (45.050, 45.005, 45.500, 45.0500)

ANSWER:

(i) 0.85 and 0.08 are not equivalent to the given decimal.

In 0.85, we have 5 in the hundredth place, whereas in 0.8, we have nothing in the hundredth place.

In 0.08, 0 is in the tenth place, whereas in 0.8, 8 is in the tenth place.

(ii) 25.01 and 25.001 are not equivalent to the given decimal.

In 25.01, 0 is in the tenth place, whereas in 25.1, 1 is in the tenth place.

In 25.001, 0 is in the tenth place, whereas in 25.1, 1 is in the tenth place.

(iii) 45.005 and 45.500 are not equivalent to the given decimal.

In 45.005, 0 is in the hundredth place, whereas in 45.05, 5 is in the hundredth place.

In 45.500, 5 is in the tenth place, whereas in 45.05, 0 is in the tenth place.

Page No 7.26:

Question 2: Which of the following are like decimals:

(i) 0.34, 0.07, 5.35, 24.70

(ii) 45.05, 4.505, 20.55, 20.5

(iii) 8.80. 17.08, 8.94, 0.27

(iv) 4.50, 16.80, 0.700, 7.08
ANSWER: (i) Like decimals, since these have the same number of digits after the decimal  point.

(ii) Unlike decimals, since these have different number of digits after the decimal point.

(iii) Like decimals, since these have the same number of digits after the decimal point.

(iv) Unlike decimals, since these have different number of digits after the decimal point.

Page No 7.26:

Question 3: Which of the following statements are correct?

(i) 8.05 and 7.95 are like decimals.

(ii) 0.95, 0.306, 7.10 are unlike decimals.

(iii) 3.70 and 3.7 are like decimals.

(iv) 13.59, 1.359, 135.9 are like decimals.

(v) 5.60, 3.04, 0.45 are like decimals.

ANSWER:

(i) Correct, since these two decimals have the same number of digits after the decimal point, only 2.

(ii) Correct, since these three decimals have different numbers of digits after the decimal point.

(iii) Incorrect, since these two decimals have different numbers of digits after the decimal point.

(iv) Incorrect, since these three decimals have different numbers of digits after the decimal point.

(v) Correct, since these three decimals have the same number of digits after the decimal point.

Page No 7.26:

Question 4: Convert each of the following sets of unlike decimals to like decimal:

(i) 7.8, 7.85

(ii) 2.02, 3.2

(iii) 0.6, 5.8, 12.765

(iv) 5.296, 5.2, 5.29

(v) 4.3294, 43.29, 432.94

ANSWER: (i) Of the two given decimals, 7.85 has more decimal places, i.e., two, so we change 7.8 so that it has two decimal places.

Therefore, the like decimals are 7.80 and 7.85.

(ii) Of the two given decimals, 2.02 has more decimal places, i.e., two, so we change 3.2 so that it has two decimal places.

Therefore, the like decimals are 2.02 and 3.20.

(iii) Of the three given decimals, 12.765 has the highest number of decimal places, i.e., three, so we change the other two decimals so that they also have three decimal places.

Therefore, the like decimals are 0.600, 5.800 and 12.765.

(iv) Of the three given decimals, 5.296 has the highest number of decimal places, i.e., three, so we change the other two decimals so that they also have three decimal places.

Therefore, the like decimals are 5.296, 5.200 and 5.290.

(v) Among the three given decimals, 4.3294 has the highest number of decimal places, i.e., four, so we change all the decimals so that they also have four decimal places.

Therefore, the like decimals are 4.3294, 43.2900 and 432.9400.

Page No 7.28:

Question 1: Find the sum in each of the following:

ANSWER:

(i)  102.360

+       7.054

+       0.800

=   110. 214

(ii)    0.060

 +     4.108

 +   91.500

=    95.668

(iii)   312.800

+      290.020

+      128.457

=      731.277

(iv)   113.285

+         6.700

+         9.340

+       30.080

=     159.405   

(v)      3.420

+    264.080

+       7.600

+     95.321   

=   370.421

(vi)    18.0030

+       41.7000

+       10.9500

+         5.0570

=       75.7100

Page No 7.29:

Question 2: Add the following

(i) 41.8, 39.24, 5.01 and 62.6

(ii) 4.702, 4.2, 6.02 and 1.27

(iii) 18.03, 146.3, 0.829 and 5.324

ANSWER:

(i)    41.80

+     39.24

+       5.01

+     62.60

=   148.65

(ii)       4.702

    +     4.200

    +     6.020  

    +     1.270

=       16.192

(iii)    18.030

+     146.300

+         0.829

+         5.324

=     170.483

Page No 7.29:

Question 3: Find the sum in each of the following:

(i) 0.007 + 8.5 + 30.08

(ii) 280.69 + 25.2 + 38

(iii) 25.65 + 9.005 + 3.7

(iv) 27.076 + 0.55 + 0.004

ANSWER:

(i)   0.007

+    8.500

+  30.080

=  38.587

(ii)  280.69

+      25.20

+      38.00

=    343.89

(iii)  25.650

 +      9.005

 +      3.700

 =    38.355

(iv)    27.076

+        0.550

+        0.004

=      27.630

Page No 7.29:

Question 4: Radhika's mother gave her Rs 10.50 and her father gave her Rs 15.80, find the total amount given to Radhika by her parents.

ANSWER:
Radhika's mother gave her Rs 10.50.

Radhika's father gave her Rs 15.80.

Total amount given to Radhika =

        10.50

      +15.80

= Rs 26.30

Page No 7.29:

Question 5: Rahul bought 4 kg 90 g apples, 2 kg 60 g of grapes and 5 kg 300 g mangoes. Find the weight of the fruits he bought in all.

ANSWER:

Weight of apples = 4 kg 90 g = 4.090 kg

Weight of grapes = 2 kg 60 g = 2.060 kg

Weight of mangoes = 5 kg 300 g =5.300 kg

Therefore, total weight of fruits bought by Rahul =

    4.090 kg

    2.060 kg

+  5.300 kg

=  11.450 kg

Total weight of the fruits  = 11.450 kg

Page No 7.29:

Question 6: Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for skirt. Find the total cloth bought by her.

ANSWER:

Cloth for shirt = 3 m 20 cm = 3.20 m       (we know that 1 m = 100 cm )

Cloth for  skirt = 2 m 5 cm= 2.05 m

Total cloth bought by Nasreen =

   3.20 m

+ 2.05 m

= 5.25 m

Total cloth bought  = 5.25 m

Page No 7.29:

Question 7: Sunita travels 15 km 268 m by bus, 7 km 7 m by car and 500 m by foot in order to reach her school. How far is her school from her residence?

ANSWER:

Travel by bus = 15 km 268 m= 15.268 km (we know that 1 km = 1000 m)

Travel by car = 7 km 7 m = 7.007 km

Travel on foot = 500 m = 0.500 km

Total distance travelled =

 15.268 km

   7.007 km

+ 0.500 km

= 22.775 km

Therefore, Sunita's school is 22.775 km from her residence.

Page No 7.31:

Question 1: Subtract:

ANSWER:

(i)   46.23

    - 37.50

   =  8.73

(ii)   128.40

    -    53.05

=       75.35

(iii) 45.03

    - 27.80

   =17.23

(iv)   23.930 

 -        5.946

=      17.984

Page No 7.31:

Question 2: Find the value of:

(i) 9.756 − 6.28

(ii) 21.05 − 15.27

(iii) 18.5 − 6.79

(iv) 48.1 − 0.37

(v) 108.032 − 86.8

(vi) 91.001 − 72.9

(vii) 32.7 − 25.86

(viii) 100 − 26.32

ANSWER:

(i)      9.756

   −     6.280

   =    3.476

(ii)    21.05

  −     15.27

  =     5.78

(iii)    18.50

 −        6.79

=       11.71

(iv)    48.10

 −        0.37

=       47.73

(v)     108.032

      −   86.800

     =    21.232

(vi)  91.001

     −72.900

    = 18.101

(vii)  32.70

 −     25.86

=       6.84

(viii)  100.00

  −      26.32

=        73.68

Page No 7.31:

Question 3: The sum of two numbers is 100. If one of them is 78.01, find the order.

ANSWER:

One number is 78.01.

Suppose the other number is x.

The sum of these numbers is 100.

Therefore, 78.01 + x= 100.

 x= 100 - 78.01

 = 21.99

The other number is 21.99.

Page No 7.31:

Question 4: Waheeda's school is at a distance of 5 km 350 m from her house. She travels 1 km 70 m on foot and the rest she travels by bus. How much distance does she travel by bus?
ANSWER:

Distance travelled on foot = 1 km 70 m = 1.070 km (we know that 1 km = 1000 m)

Suppose distance travelled by bus = x km

Total distance of school from residence = 5 km 350 m = 5.350 km

So, 1.070 + x = 5.350

x= 5.350 - 1.070

x= 4.280 km

Therefore, distance travelled by bus = 4.280 km

Page No 7.31:

Question 5: Raju bought a book for Rs 35.65. He gave Rs 50 to the shopkeeper. How much money did he get back from the shopkeeper?

ANSWER:

Price of the book = Rs 35.65

Amount given to the shopkeeper = Rs 50

Therefore, balance returned by the shopkeeper

= Rs 50 - Rs 35.65

= Rs 14.35

Page No 7.31:

Question 6: Ruby bought a watermelon weighing 5 kg 200 g. Out of this she gave 2 kg 750 g to her neighbour. What is the weight of the watermelon left with Ruby?

ANSWER: Weight of the watermelon when bought = 5 kg 200 g = 5.200 kg (we know that 1 kg = 1000 g)

Weight of the watermelon given to the neighbour  = 2 kg 750 g= 2.750 kg

Therefore, weight of the watermelon left with Ruby = Weight of the watermelon when bought - weight of the watermelon given to the neighbour

= 5.200 kg - 2.750 kg

= 2.450 kg

So, weight of the watermelon left with Ruby = 2.450 kg

Page No 7.32:

Question 7: Victor drove 89.050 km on Saturday and 73.9 km on Sunday. How many kilometres more did he drive on Saturday?

ANSWER:

Distance travelled on Saturday = 89.050 km

Distance travelled on Sunday = 73.9 km

Subtracting the distance travelled on Sunday from the distance travelled on Saturday

89.050 km - 73.9 km

= 15.15 km

Therefore, Victor drove 15.15 km more on Saturday.

Page No 7.32:

Question 8: Raju bought a book for Rs 35.65 and a pencil box for Rs 9.35. He gave Rs 50 to the shopkeeper. How much money did he get back from the shopkeeper?

ANSWER:

Cost of a book = Rs 35.65

Cost of a pencil = Rs 9.35

Total cost = 35.65 + 9.35 = Rs 45.00

Amount that Raju gave to shopkeeper = Rs 50

Balance amount he would get = 50.00 −- 45.00 = Rs 5.

Page No 7.32:

Question 9: Gopal travelled 125.5 km by bus, 14.25 km by pony and the rest of distance of Kedarnath on foot. If he covered a total distance of 150 km, how much did he travel on foot?

ANSWER:
Distance travelled by bus = 125.5 km

Distance travelled on pony = 14.25 km

Suppose the distance travelled on foot = x

Total distance = 150 km = Distance travelled by bus + distance travelled on pony + distance travelled on foot

150 km = 125.5 km + 14.25 km + x

150 km = 139.75 km + x

x = 150 km - 139.75 km

x=  10.25 km

Therefore, distance travelled on foot = 10.25 km

Page No 7.32:

Question 10: Tina had 20 m 5 cm long cloth. She cuts 4 m 50 cm length of cloth form this for making a curtain. How much cloth is left with her?

ANSWER: 
Length of cloth originally = 20 m 5 cm = 20.05 m (we know that 1 m = 100 cm)
Length of cloth cut for curtain = 4 m 50 cm = 4.50 m

Therefore, length of cloth left with Tina = Length of cloth originally - length of cloth cut for curtain

20.05 - 4.50

= 15.55 m

Length of cloth left with Tina = 15.55 m

Page No 7.32:

Question 11: Vineeta bought a book for Rs 18.80, a pen for Rs 8.50 and some papers for Rs 5.05. She gave fifty rupee to the shopkeeper. How much balance did she get back?

ANSWER:

Price of the book = Rs 18.90

Price of the pen = Rs 8.50

Price of the paper = Rs 5.05

Total price of the three items = Rs 18.90 + Rs 8.50 + Rs 5.05

= Rs 32.45

Total amount given to the shopkeeper = Rs 50

Therefore, balance received from the shopkeeper

= Total amount given to the shopkeeper - total price of the three items

= Rs 50 - Rs 32.45

= Rs 17.55

Page No 7.32:

Question 12: Tanuj walked 8.62 km on Monday, 7.05 km on Tuesday and some distance on Wednesday. If he walked 21.01 km in three days, how much distance did he walk on Wednesday?

ANSWER:

Distance travelled on Monday = 8.62 km

Distance travelled on Tuesday = 7.05 km

Suppose the distance travelled on Wednesday = x km

Total distance travelled in three days  = Distance travelled on (Monday + Tuesday + Wednesday)

21.01 = 8.62 + 7.05 + x

21.01 = 15.67 + x

x = 21.01 - 15.67 = 5.34

Therefore, Tanuj walked 5.34 km on Wednesday.

Page No 7.32:

Question 1:

(a) 3.1

(b) 1.3

(c) 0.3

(d) 0.03

ANSWER:

(c) 0.3

3/10 is equal to 0.3. Since the denominator is 10, we have to mark the decimal such that 3 is in the tenth place.

Page No 7.32:

Question 2:

(a) 7.1

(b) 7.01

(c) 0.7

(d) 0.07

ANSWER:

(d) 0.07

7/100 is equal to 0.07. Since the denominator is 100, we have to mark the decimal such that 7 is in the hundredth place.

Page No 7.32:

Question 3:

(a) 0.004

(b) 0.04

(c) 0.4

(d) 4.001

ANSWER:

(a) 0.004

Since the denominator is 1000, we have to mark the decimal such that 4 is in the thousandth place.

Page No 7.32:

Question 4:

The value of  is

(a) 0.0370

(b) 0.0037

(c) 0.00037

(d) 0.000037

ANSWER:

(b) 0.0037

Since the denominator is 10000, we have to mark the decimal such that 3 is in the thousandth place and 7 is in the ten-thousandth place.

Page No 7.32:

Question 5: The place value of 5 in 0.04532 is

ANSWER:

5 is in the thousandth place.

0.04532 = 4/100 + 5/1000 + 3/10000 + 2/100000

Page No 7.32:

Question 6: The value of  is

(a) 0.231

(b) 2.31

(c) 23.1

(d) 0.0231

ANSWER:

(a) 0.231

We have 2 tenths, 3 hundredths and 1 thousandth.

Therefore, the value of 231/1000 is 0.231.

Page No 7.32:

Question 7: The value of  is

(a) 3.5

(b) 3.05

(c) 3.005

(d) 3.0005

ANSWER:

(c) 3.005

Page No 7.33:

Question 8:
The value of  is

(a) 1.2

(b) 0.12

(c) 0.012

(d) None of these

ANSWER:

(b) 0.12

Page No 7.33:

Question 9: The value of is

a) 2.4

(b) 2.25

(c) 2.04

(d) 2.40

ANSWER:

(c) 2.04

Page No 7.33:

Question 10: is equal to

(a) 4.78

(b) 4.87

(c) 4.875

(d) None of these

ANSWER:

(c) 4.875

Page No 7.33:

Question 11:  is equal to

(a) 2.305

(b) 2.3

(c) 2.35

(d) 0.235

ANSWER:

(c) 2.35

3/10 = 0.3 (since the denominator is 10, we need to mark the decimal such that 3 is in the tenth place)

5/100= 0.05 (since the denominator is 100, we need to mark the decimal such that 5 is in the hundredth place)

Therefore, 2 + 3/10 + 5/100 = 2+ 0.3 + 0.05

= 2.35

Page No 7.33:

Question 12:  is equal to

(a) 0.35

(b) 0.305

(c) 0.0305

(d) 0.3005

ANSWER:

(c) 0.0305

3/100 = 0.03 (here, we have the denominator 100, so we mark the decimal such that 3 is in the hundredth place)

5/10000 = 0.0005 (here, we have the denominator 10000, so we mark the decimal such that 5 is in the ten thousandth place)

Therefore, 3/100 + 5/10000 = 0.03 + 0.0005

= 0.0305

Page No 7.33:

Question 13: 1 cm is equal is

(a) 0.1 m

(b) 0.01 m

(c) 0.10 m

(d) 0.001 m

ANSWER:

(b) 0.01 m

We know that 100 cm = 1 m.

Therefore, 1 cm = 1/100 m = 0.01 m.

Page No 7.33:

Question 14: 1 m is equal to

(a) 0.1 km

(b) 0.01 km

(c) 0.001 km

(d) 0.0001 km

ANSWER:

(c) 0.001 km

We  know that 1000 m = 1 km.

Therefore, 1 m = 1/1000 m = 0.001 km.

Page No 7.33:

Question 15: 2 kg 5 gm is equal to

(a) 2.5 kg

(b) 2.05 kg

(c) 2.005 kg

(d) 2.6 kg

ANSWER:

(c) 2.005 kg

We know that 1000 g = 1 kg.

       Therefore,    1 g = 1/1000 kg = 0.001 kg

                           5 g = 5/1000 kg = 0.005 kg

       Therefore, 2 kg 5 gm

             =2 kg + 0.005 kg

             = 2.005 kg

Page No 7.33:

Question 16: 15 litres and 15 ml is equal to

(a) 15.15 litres

(b) 15.150 litres

(c) 15.0015 litres

(d) 15.015 litres

ANSWER:

(d) 15.015 litres

We know that 1000 ml = 1 litre.

Therefore,    1 ml = 1/1000 = 0.001 litre

                   15 ml = 15/1000 = 0.015 litre

So, 15 litre and 15 ml

      = 15 litre  + 0.015 litre

      = 15.015 litres

Page No 7.33:

Question 17: Which of the following are like decimals?

(a) 5.5, 5.05, 5.005, 5.50

(b) 5.5, 0.55, 5.55, 5.555

(c) 5.5, 6.6, 7.7, 8.8

(d) 0.5, 0.56, 0.567, 0.5678

ANSWER: (c) 5.5. 6.6, 7.7, 8.8 are like decimals, since the number of decimals is the same.

Page No 7.33:

Question 18: The value of 0.5 + 0.005 + 5.05 is

(a) 5.55

(b) 5.555

(c) 5.055

(d) 5.550

ANSWER:

(b) 5.555

Page No 7.33:

Question 19: 0.35 − 0.035 is equal to

(a) 0.3

(b) 0.349

(c) 0.315

(d) 0.353

ANSWER:

(c) 0.315

 0.350

− 0.035

=0.315

Page No 7.33:

Question 20: 2.5 + 3.05 − 4.005 is equal to

(a) 1.545

(b) 1.455

(c) 1.554

(d) 0.545

ANSWER:

(a) 1.545

2.5 + 3.05 − 4.005

= 5.55 − 4.005

= 1.545

Page No 7.33:

Question 21: Which is greater among 2.3, 2.03, 2.33, 2.05?

(a) 2.3

(b) 2.03

(c) 2.33

(d) 2.05

ANSWER:

(c) 2.33

The whole parts of all the above numbers are equal. Comparing the tenth parts, we see that two of the decimals have a tenth part 0 and two have a tenth part 3. Leaving aside the decimals that have a tenth part 0, we have 2.3 and 2.33. Comparing them, we find that 2.33 is greater than 2.3, because, in 2.3, there is no hundredth part, but in 2.33, the hundredth part is 3.

Page No 7.33:

Question 1: The fraction  in decimal form is

(a) 0.09

(b) 9.1

(c) 1.9

(d) 0.9

ANSWER:

The fractionin decimal form is 0.9

Hence, the correct option is (d).

Page No 7.34:

Question 2: The fraction in decimal form is
(a) 7.1

(b) 7.01

(c) 0.7

(d) 0.07

ANSWER:

The fraction in decimal form is 0.07.

Hence, the correct option is (d).

Page No 7.34:

Question 3: The fraction in decimal form is

(a) 0.3

(b) 0.03

(c) 0.003

(d) 1.003

ANSWER: The fraction  in decimal form is 0.003.

Hence, the correct option is (c).

Page No 7.34:

Question 4: The fraction  indecimal form is

(a) 17.3

(b) 1.73

(c) 0.173

(d) 0.0173

ANSWER:

The fraction in decimal form is 0.173.

Hence, the correct option is (c).

Page No 7.34:

Question 5: The value of  in decimal form is

(a) 2.19

(b) 2.019

(c) 0.219

(d) 21.9

ANSWER:

Hence, the correct option is (a).

Page No 7.34:

Question 6: 31.08 as a mixed fraction is

ANSWER:

Hence, the correct option is (b).

Page No 7.34:

Question 7: 

(a) 2.304

(b) 0.403

(c) 2.34

(d) 2.43

ANSWER:

Hence, the correct option is (c).

Page No 7.34:

Question 8:

(a) 0.35

(b) 0.305

(c) 0.0305

(d) 0.035

ANSWER:

Hence, the correct option is (c).

Page No 7.34:

Question 9:

(a) 0.53

(b) 0.053

(c) 0.35

(d) 0.035

ANSWER:

Hence, the correct option is (a).

Page No 7.34:

Question 10: 9.02 − 5.7 = ?
(a) 3.32

(b) 3.23

(c) 2.32

(d) None of these

ANSWER:

9.02 − 5.7 =

Hence, the correct option is (a).

Page No 7.34:

Question 11: Convert into a decimal fraction.

ANSWER:

Hence, the value of 29402940 into a decimal fraction is 2.225.

Page No 7.34:

Question 12: Convert the following decimals into fractions in simplest form:

(i) 0.025

(ii) 0.35

(iii) 0.075

ANSWER:

Page No 7.34:

Question 13: What number subtracted from 18.5 gives 6.2376?

ANSWER:

Let the required number be x.

According to the question,

Hence, 12.2624 subtracted from 18.5 gives 6.2376.

Page No 7.34:

Question 14: Arrange the following decimal numbers in the ascending order

0.52314, 0.52313, 0.53201, 0.52321

ANSWER:

Here, the hundredth part of 0.53201 is greater than all others.

So, the greatest number is 0.53201.

Now, in numbers 0.52314, 0.52313 and 0.52321,

they all have same parts upto thousandth.

But the ten thousandths part of 0.52321 is greater than the other two.

Now, in numbers 0.52314 and 0.52313,

they all have same parts upto ten thousandth.

But the hundred thousandths part of 0.52314 is greater than that of 0.52313.

Hence, 0.52313 < 0.52314 < 0.52321 < 0.53201

Page No 7.34:

Question 15: Convert the following decimals as fractions:

(i) 2.3675

(ii) 54.26

(iii) 75.35

(iv) 0.7575

ANSWER:

Page No 7.34:

Question 16: By how much should 27.354 be increased to get 52?

ANSWER: Let the required value be x.

According to the question,

27.354 + x = 52

⇒ x = 52 − 27.354

  Hence, 24.646 should 27.354 be increased to get 52.

Page No 7.34:

Question 17: Shikha bought 2 m 5 cm cloth for her salwar and 3 m 35 cm cloth for her shirt. Find the total length of cloth bought by her.

ANSWER:

Cloth required for salwar = 2 m 05 cm = 2.05 m

Cloth required for shirt = 3 m 35 cm = 3.35 m

Total cloth required is

Hence, the total length of cloth bought by Shikha is 5.4 m.

Page No 7.35:

Question 18: Suman purchased 5 kg 75 g of fruits and 3 kg 465 g of vegetables, and put them in a bag. If this bag with these contents weighs 9 kg, find the weight of the empty bag.

ANSWER:

Weight of fruits = 5 kg 75 g = 5.075 kg

Weight of vegetables = 3 kg 465 g = 3.465 kg

Total weight of fruits and vegetables is

Now, the bag with these contents weighs 9 kg.

Therefore, the weight of empty bag is

Hence, the weight of the empty bag is 460 g.

Page No 7.35:

Question 19: Evaluate the following:

36.36 − 28.4237 − 9.78 + 7.7

ANSWER:

36.36 − 28.4237 − 9.78 + 7.7

= 36.36 + 7.7 − (28.4237 + 9.78)

= 44.06 − 38.2037

= 5.8563

Page No 7.35:

Question 20: What number added to 3.56 gives 23.018?

ANSWER:

Let the required number be x.

According to the question,

3.56 + x = 23.018

⇒ x = 23.018 − 3.56

⇒ x = 19.458

Hence, 19.458 when added to 3.56 gives 23.018.

Page No 7.35:

Question 21: Fill in the blanks:

ANSWER:

Thus, 3410000=0.00343410000=0.0034.

Page No 7.35:

Question 22: Fill in the blanks:

ANSWER:

1 km = 1000 m

Page No 7.35:

Question 23:

Fill in the blanks:

ANSWER:

1 kg = 1000 g

⇒1 g=11000kg⇒1 g=11000kg

Page No 7.35:

Question 24:

Fill in the blanks:

ANSWER:

1 l = 1000 ml

Page No 7.35:

Question 25:

Fill in the blanks:

ANSWER:

1 m = 100 cm

Page No 7.4:

Question 1: Write the following decimals in the place value table:

(i) 52.5

(ii) 12.57

(iii) 15.05

(iv) 74.059

(v) 0.503

ANSWER:

The given decimals can be written as above in the place-value table.

Page No 7.5:

Question 2: Write the decimals shown in the following place value table:

ANSWER:

The decimals shown in the above place-value table can be written as follows.

(i)    307.12

(ii)   9543.025

(iii)  12.503

Page No 7.5:

Question 3: Write each of the following decimals in words:

(i) 175.04

(ii) 0.21

(iii) 9.004

(iv) 0.459

ANSWER:

(i) One hundred seventy-five and four hundredths

(ii) Zero and twenty-one hundredths

(iii) Nine and four thousandths

(iv) Zero and four hundred fifty-nine thousandths

Page No 7.5:

Question 4: Write each of the following as decimals:

ANSWER:

1)  We have 6 tens, 5 ones, 2 tenths and 7 hundredths.

Therefore, the decimal number is 65.27.

2) We have 4 tens, 5 ones and 9 hundredths.

Therefore, the decimal number is 45.09.

3) We have 8 tens, 8 ones, 5 tenths and 2 thousandths.

Therefore, the decimal number is 88.502.

4)  We have 3 tenths and 7 thousandths.

Therefore, the decimal number is 0.307.

Page No 7.5:

Question 5: Write each of the following as decimals:

(i) Five and four tenths
(ii) Twelve and four hundredths
(iii) Nine and Seven hundred five thousandths
(iv) Zero point five two six
(v) Forty seven and six thousandths
(vi) Eight thousandths

(vii) Nineteen and nineteen hundredths.
ANSWER:

Page No 7.9:

Question 1: Write each of the following as decimals:

(i) Three tenths

(ii) Two ones and five tenths

(iii) Thirty and one tenths

(iv) Twenty two and six tenths

(v) One hundred, two ones and three tenths

ANSWER:

(i) 310310 = 0.3

(ii) 2 + 510510 = 2.5

(iii) 30 + 110110 = 30.1

(iv) 22 + 610610 = 22.6

(v) 100 + 2 + 310310 = 102.3

Page No 7.9:

Question 2: Write each of the following as decimals:

ANSWER:
(i) We have 3 tens, 6 ones and 2 tenths.

Therefore, the decimal is 36.2 

(ii) We have 7 hundreds, 5 ones and 7 tenths.

Therefore, the decimal is 705.7.

(iii) We have 2 hundreds, 6 tens, 5 ones and 1 tenths.

Therefore, the decimal is 265.1.

(iv) We have 2 hundreds, 7 tens , 9 ones and 5 tenths.

Therefore, the decimal is 279.5.

Page No 7.9:

Question 3: Write each of the following as decimals:

ANSWER:

Since the denominator is ten, the decimal is 2.2.

(ii)  3/2

Making the denominator 10, we have

3/2

(iii)  2/5

Making the denominator 10, we have

2/5

Page No 7.9:

Question 4: Write each of the following as decimals:

ANSWER:

To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus, we get



Here, the denominator is 10.

Therefore, the decimal is 39.2.

To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus, we get

To write in decimal, we need to make the denominator 10 by multiplying it by a number. But, to maintain the value of the fraction, we should also multiply the numerator by the same number. Thus, we get

Page No 7.9:

Question 5: Write the following decimal as fractions. Reduce the fractions to lowest form:

(i) 3.8

(ii) 21.2

(iii) 6.4

(iv) 1.0

ANSWER:

(iv)  1.0

Since the only number after the decimal is 0, the fraction is 1.

Page No 7.9:

Question 6: Represent the following decimal numbers on the number line:

(i) 0.2

(ii) 1.9

(iii) 1.1

(iv) 2.5

ANSWER:

Page No 7.9:

Question 7: Between which two whole numbers on the number line are the given numbers? Which one is nearer the number?

(i) 0.8

(ii) 5.1

(iii) 2.6

(iv) 6.4

(v) 9.0

(vi) 4.9

ANSWER:

(i) 0.8 is between the two whole numbers 0 and 1.

     As 0.8 is 8 units from 0 and 2 units from 1, it is nearer to 1.

(ii) 5.1 is between the two whole number 5 and 6.

      As 5.1 is 1 unit from 5 and 9 units from 6, it is nearer to 5.

(iii) 2.6 is between 2 and 3.

      As 2.6 is 6 units from 2 and 4 units from 3, it is nearer to 3.

(iv) 6.4 is between 6 and 7.

      As 6.4 is 4 units from 6 and 6 units from 7, it is nearer to 6.

(v) 9.0 is itself a whole number, that is, 9.

(vi) 4.9 is between 4 and 5.

     As 4.9 is 9 units from 4 and 1 unit from 5, it is nearer to 5.

Page No 7.9:

Question 8:

Write the decimal number represented by the points on the given number line: A,B,C,D.

ANSWER:

A) 0.8, since A  is at the eighth place between 0 and 1

B) 1.3, since B is at the third place between 1 and 2
C) 1.9, since C is at the ninth place between 1 and 2

D) 2.6, since D is at the sixth place between 2 and 3

Disclaimer: The image given in the book is not consistent, as the number of periods between 0 and 1 is ten but the number of periods between 1 and 2 is seven. So, ignoring the position of the given numbers 1 , 2 and 3, it has been assumed that there are ten periods between every two consecutive numbers starting from the first point taken as zero.