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51.

Find the product: 2.9 × 100

Answer»

2.9 × 100

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

2.9 × 100 = 290

52.

Find the product: 0.83 × 10

Answer»

0.83 × 10

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

0.83 × 10 = 8.3

53.

Find the product:  0.08 × 100

Answer»

0.08 × 100

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

0.08 × 100 = 8

54.

Find the product:  0.6 × 100

Answer»

 0.6 × 100

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

0.6 × 100 = 60

55.

Find the product: 6.7314 × 1000

Answer»

6.7314 × 1000

On multiplying a decimal by 1000, the decimal point is shifted to the right by three places.

We have,

6.7314 × 1000 = 6731.4

56.

Find the product: 84.003 × 10

Answer»

84.003 × 10

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

84.003 × 10 = 840.03

57.

Find the product: 0.06 × 100

Answer»

0.06 × 100

On multiplying a decimal by 100, the decimal point is shifted to the right by two places.

We have,

0.003 × 100 = 0.3

58.

Find the product: 7.54 × 10

Answer»

7.54 × 10

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

7.54 × 10 = 75.4

59.

Find the product: 73.92 × 10

Answer»

73.92 × 10

On multiplying a decimal by 10, the decimal point is shifted to the right by one place.

We have,

73.92 × 10 = 739.2

60.

Add: 23.8, 8.94, 0.078 and 214.6

Answer»

23.8, 8.94, 0.078 and 214.6

First convert the given decimals into like decimals.

We get,

23.800, 8.940, 0.078 and 214.600

Write the addends on under the other in column form, keeping the decimal points of all the addends in the same column and the digits of the same place in the same column.

Writing these decimals in column from and adding, we get:

23.800

8.940

0.078

214.600

________________

247.418

________________

Hence, the sum of the given decimals is 247.418

61.

Subtract: 13.876 from 22

Answer»

13.876 from 22

Converting the decimals into like decimals, we get 13.876 from 22.000

Writing them into column form with the larger one at the top and subtracting, we get:

22.000

-13.876

_____________

8.124

_____________

Hence (13.876-22) = 8.124

62.

Subtract: 36.74 from 52.6

Answer»

36.74 from 52.6

Converting the decimals into like decimals, we get 36.74 and 52.60

Writing them into column form with the larger one at the top and subtracting, we get:

52.60

-36.74

_____________

15.86

_____________

Hence (36.74 – 52.6) = 15.86

63.

Add: 26.9, 19.74, 231.769 and 0.048

Answer»

26.9, 19.74, 231.769 and 0.048

First convert the given decimals into like decimals.

We get,

26.900, 19.740, 231.769 and 0.048

Write the addends on under the other in column form, keeping the decimal points of all the addends in the same column and the digits of the same place in the same column.

Writing these decimals in column from and adding, we get:

26.900

19.740

234.769

0.048

______________

278.457

______________

Hence, the sum of the given decimals is 278.457

64.

Take out of 3.547 from 7.2.

Answer»

Given 3.547 from 7.2

7.2

– 3.547

3.653

65.

Find the product:(i) 4.74 × 10(ii) 0.45 × 10(iii) 0.0215 × 10(iv) 0.0054 × 10

Answer»

(i) Given 4.74 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 4.74 × 10 = 47.4

(ii) Given 0.45 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 0.45 × 10 = 4.5

(iii) Given 0.0215 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 0.0215 × 10 = 0.215

(iv) Given 0.0054 × 10

Here we have to do normal multiplication with shifting the decimal point by one place to the right

Therefore 0.0054 × 10 = 0.054

66.

By how much should 59.71 be decreased to get 34.58?

Answer»

Let x be the unknown number

59.71 – x =34.58

59.71 – 34.58 = x

x = 59.71 – 34.58

x = 25.13

25.13 should be decreased by 59.71 to get 34.58

67.

What is to be added to 36.85 to get 59.41?

Answer»

Given 36.85 and 59.41

Let the unknown number be x

x + 36.85 = 59.41

x = 59.41 – 36.85

x = 22.56

Hence 22.56 is to be added to 36.85 to get 59.41

68.

Find the product:(i) 3.14 × 17(ii) 0.745 × 12(iii) 28.73 × 47(iv) 0.0415 × 59

Answer»

(i) Given 3.14 × 17

First multiply as usual without looking at the decimal point

3.14 × 17 = 578

Now mark the decimal point in the product to have one place of decimal as there in the given decimal

3.14 × 17 = 57.8

(ii) Given 0.745 × 12

First multiply as usual without looking at the decimal point

0.745 × 12 = 894

Now mark the decimal point in the product to have three places of decimal as there in the given decimal

0.745 × 12 = 8.94

(iii) Given 28.73 × 47

First multiply as usual without looking at the decimal point

28.73 × 47 = 135031

Now mark the decimal point in the product to have two places of decimal as there in the given decimal

28.73 × 47 = 1350.31

(iv) Given 0.0415 × 59

First multiply as usual without looking at the decimal point

0.0415 × 59 = 24485

Now mark the decimal point in the product to have four places of decimal as there in the given decimal

0.0415 × 59 = 2.4485

69.

Find:(i) 1.07 × 0.02(ii) 211.9 × 1.13(iii) 10.05 × 1.05(iv) 13.01 × 5.01

Answer»

(i) Given 1.07 × 0.02

First multiply as usual without looking at the decimal point

1.07 × 0.02 = 00214

Sum of the decimals is 4

Now mark the decimal point in the product to have four places of decimal as there in the given decimal

1.07 × 0.02 = 0.0214

(ii) Given 211.9 × 1.13

First multiply as usual without looking at the decimal point

211.9 × 1.13 = 239447

Sum of the decimals is 3

Now mark the decimal point in the product to have three places of decimal as there in the given decimal

211.9 × 1.13 = 239.447

(iii) Given 10.05 × 1.05

First multiply as usual without looking at the decimal point

10.05 × 1.05 = 105525

Sum of the decimals is 4

Now mark the decimal point in the product to have four places of decimal as there in the given decimal

10.05 × 1.05 = 10.5525

(iv) Given 13.01 × 5.01

First multiply as usual without looking at the decimal point

13.01 × 5.01 = 651801

Sum of the decimals is 4

Now mark the decimal point in the product to have four places of decimal as there in the given decimal

13.01 × 5.01 = 65.1801

70.

Find the product: 11.1 × 1.1 × 0.11

Answer»

11.1 × 1.1 × 0.11

First we find the product of 111 × 11 × 11

Now,

=111 × 11 = 1221

= 1221 × 11= 13431

Sum of decimal places in the given decimals = 4

So, the product must contain 3 places of decimals.

∴ 11.1 × 1.1 × 0.11= 1.3431

71.

What should be added to 3.07 to get 3.5?a) 0.57 b) 0.34 c) 0.43 d) 0.02

Answer»

c) 0.43

Let us assume the missing number be x,

Then,

= 3.07 + x = 3.5

By sending 3.07 from left hand side to the right hand side it become -3.07. We get,

= 3.5 – 3.07 = x

= 0.43

72.

Divide: 0.02 by 100

Answer»

0.02 by 100

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

We have,

= 0.02 ÷ 100

= (0.02/100)

= 0.0002

73.

Find the product: 0.2 × 0.02 × 0.002

Answer»

0.2 × 0.02 × 0.002

First we find the product of 2 × 2 × 2

Now,

=2 × 2 = 4

= 4 × 2= 8

Sum of decimal places in the given decimals = 6

So, the product must contain 3 places of decimals.

∴ 0.2 × 0.02 × 0.002= 0.000008

74.

Add the following:(i) 41.8, 39.24, 5.01 and 62.6(ii) 18.03, 146.3, .829 and 5.324

Answer»

(i) Given 41.8, 39.24, 5.01 and 62.6

41.8

39.2

5.01

+ 62.6

148.65

(ii) Given 18.03, 146.3, 0.829 and 5.324

18.03

146.3

0.829

+ 5.324

170.483

75.

(1.007- 0.7) = ?a) 1 b) 0.37 c) 0.307 d) none of these

Answer»

c) 0.307

First convert the given decimals into like decimals

= (1.007 – 0.700)

= 0.307

76.

Divide: 1286.5 by 1000

Answer»

1286.5 by 1000

On dividing a decimal by 1000, the decimal point is shifted to the left by three places.

We have,

= 1286.5 ÷ 1000

= (1286.5/1000)

= 1.2865

77.

Divide: 0.58 by 100

Answer»

0.58 by 100

On dividing a decimal by 100, the decimal point is shifted to the left by two places.

We have,

= 0.58 ÷ 100

= (0.58/100)

= 0.0058

78.

What should be subtracted from 0.1 to get 0.03?a) 0.7 b) 0.07 c) 0.007 d) none of these

Answer»

b) 0.07

Let us assume the missing number be x,

Then,

= 0.1 – x = 0.03

By sending – x from left hand side to the right hand side it become x and 0.03 from right hand side to the left hand side it become -0.03. We get,

= 0.1 – 0.03 = x

= 0.07

79.

Find the product: 2.1 × 0.21 × 0.021

Answer»

2.1 × 0.21 × 0.021

First we find the product of 21 × 21 × 21

Now,

=21 × 21 = 441

= 441 × 21= 9261

Sum of decimal places in the given decimals = 6

So, the product must contain 3 places of decimals.

∴ 2.1 × 0.21 × 0.021= 0.009261

80.

Evaluate: (1.2)2

Answer»

(1.2)2

The above question can be written as, (1.2) × (1.2)

First we find the product of,

= (12) × (12) = 144

Sum of decimal places in the given decimals = 2

So, the product must contain 2 places of decimals

∴ (1.2)2 = 1.44

81.

Find the area of a rectangle whose length is 5.5m and breadth is 3.4m.

Answer»

Given length of rectangle = 5.5m

Breadth of rectangle = 3.4 m

Area of rectangle = length × breadth

= 5.5 × 3.4

= 18.7 m2

82.

By how much should 34.79 be increased to get 70.15?

Answer»

Let x be the unknown number

x + 34.79 = 70.15

x = 70.15 – 34.79

x = 35.36

35.36 should be increased to 34.79 to get 70.15

83.

Between Which two Whole numbers on the number line are the given numbers lie? Which of these Whole numbers is nearer the number?(a) 0.8(b) 5.1(c) 2.6(d) 6.4(e) 9.1(f) 4.9

Answer»

(a) 0.8 lies between 0 and 1, and is nearest to 1.

(b) 5.1 lies between 5 and 6, and is nearest to 5.

(c) 2.6 lies between 2 and 3, and is nears to 3.

(d) 6.4 lies between 6 and 7, and is nears to 6.

(e) 9.1 lies between 9 and 10, and is nears to 9.

(f) 4.9 lies between 4 and 5, and is nears to 5.

84.

Find the product:(i) 2.506 × 1000(ii) 20.708 × 1000(iii) 0.0529 × 1000(iv) 1000 × 0.1

Answer»

(i) Given 2.506 × 1000

Here we have to do normal multiplication with shifting the decimal point by three places to the right

Therefore 2.506 × 1000 = 2506

(ii) Given 20.708 × 1000

Here we have to do normal multiplication with shifting the decimal point by three places to the right

Therefore 20.708 × 1000 = 20708

(iii) Given 0.0529 × 1000

Here we have to do normal multiplication with shifting the decimal point by three places to the right

Therefore 0.0529 × 1000 = 52.9

(iv) Given 1000 × 0.1

Here we have to do normal multiplication with shifting the decimal point by three places to the right

Therefore 1000 × 0.1 = 100

85.

Find the product:(i) 35.853 × 100(ii) 42.5 × 100(iii) 12.075 × 100(iv) 100 × 0.005

Answer»

(i) Given 35.853 × 100

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 35.853 × 100 = 3585.3

(ii) Given 42.5 × 100

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 42.5 × 100 = 4250

(iii) Given 12.075 × 100

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 12.075 × 100 = 1207.50

(iv) Given 100 × 0.005

Here we have to do normal multiplication with shifting the decimal point by two places to the right

Therefore 100 × 0.005 = 0.5

86.

One meter of cloth costs Rs 152.50. What is the cost of 10.75 meters of cloth?

Answer»

Given that cost of 1m cloth = Rs 152.50

Cost of 10.75 m of cloth = 152.50 × 10.75

= Rs 1639.375

87.

1)which is greater 1 or 0.99 and 1.093 or 1.092)Lata spent Rs 9.50 for buying a pen and Rs 2.50 for one pencil.How much money did she spend?

Answer» (1) `1 = 0.99+0.01`
So, `1 gt 0.99`
`1.093 = 1.092+0.001`
So, `1.093 gt 1.092`

(2) Money spent by Lata to buy a pen ` = 9.50 ` Rs
Money spent by Lata to buy a pencil ` = 2.50 ` Rs
Total money spent by Lata `= 9.50+2.50 = 12` Rs
88.

Rahul bought 4 kg 90 g of apples, 2 kg 60 g of grapes and5 kg 300 g of mangoes. Find the total weight of all the fruits he bought

Answer» Weight of apples bought by Rahul ` = ` 4 kg 90g ` = 4.090` kg
Weight of grapes bought by Rahul ` = ` 2 kg 60g ` = 2.060` kg
Weight of mangoes bought by Rahul ` = ` 5 kg 300g ` = 5.3` kg
So, total weight of fruits ` = 4.090+2.060+5.300 = 11.450` kg
89.

Fill in each of the place holders with the correct symbol > or <.(i) 78.23 ……. 69.85(ii) 3.406……3.46(iii) 5.68……5.86(iv) 14.05……14.005(v) 1.85……1.80(vi) 0.98……1.07

Answer»

(i) 78.23 ……. 69.85

By comparing whole numbers 78 > 69

∴ 78.23>69.85

(ii) 3.406……3.46

By comparing whole number, 3 = 3

By comparing the tenths place digit, 4 = 4

By comparing the hundredths place digit, 0 < 6

∴ 3.406 < 3.46

(iii) 5.68……5.86

By comparing whole number, 5 = 5

By comparing the tenths place digit, 6 < 8

∴ 5.68 < 5.86

(iv) 14.05……14.005

By comparing whole number, 14 = 14

By comparing the tenths place digit, 0 = 0

By comparing the hundredths place digit, 5 > 0

∴ 14.05 > 14.005

(v) 1.85……1.80

By comparing whole number, 1 = 1

By comparing the tenths place digit, 8 = 8

By comparing the hundredths place digit, 5 > 0

∴ 1.85 > 1.80

(vi) 0.98……1.07

By comparing whole number, 0 < 1

∴ 0.98 < 1.07

90.

Write each of the following as a decimal.(a) Three hundred six and seven-hundredths(b) Eleven point two three five(c) Nine and twenty five thousandths

Answer» (a) Three hundred six and seven-hundredths `= 306+7/100 = 306.07`

(b) Eleven point two three five ` = 11+ .235 = 11.235`

(c) Nine and twenty five thousandths ` = 9+25/1000 = 9.025`
91.

Add: 9.09, 0.909, 99.9, 9.99, 0.099

Answer»

9.09, 0.909, 99.9, 9.99, 0.099

First convert the given decimals into like decimals.

We get,

9.090, 0.909, 99.900, 9.990, 0.099

Write the addends on under the other in column form, keeping the decimal points of all the addends in the same column and the digits of the same place in the same column.

Writing these decimals in column from and adding, we get:

9.090

0.909

99.900

9.990

0.099

____________

119.988

_____________

Hence, the sum of the given decimals is 119.988.

92.

Write each of the following as decimals:(a) Seven – tenths(b) Two tens and nine – tenths(c) Fourteen point six(d) One hundred and two ones(e) Six hundred point eight

Answer»

(a) Seven – tenths

7/10 = 0.7

(b) Two tens and nine – tenths

20 + 9/10 = 20.9

(c) Fourteen point six

14.6

(d) One hundred and two ones

100 + 2 = 102.0

(e) Six hundred point eight

600.8

93.

Subtract :(a) Rs 18.25 from Rs 20.75(b) 202.54 m from 250 m(c) Rs 5.36 from Rs 8.40(d) 2.051 km from 5.206 km(e) 0.314 kg from 2.107 kg

Answer» (a) `20.75` Rs `-` `18.25` Rs` = 2.50` Rs
(b)`250m -202.54m = 47.46 m`
(c) `8.40` Rs `-` `5.36` Rs` = 3.04` Rs
(d) `5.206` km `-` `2.051`km `= 3.155` km
(e) ` 2.107` kg `-` `0.314` kg `= 1.793` kg
94.

Convert 6.004 as a mixed fraction.

Answer»

6.004

Now write the given decimal without the decimal point as the numerator of the fraction.

In the denominator, write 1 followed by as many zeros as there are decimal places in the given decimal.

Then we have,

= 6.004 = (6004/1000)

Now reduce the above fraction to the simplest form.

= (6004/1000) … [÷ by 2]

= (1501/250)

= [6(1/250)]

95.

Convert 5.6 as a mixed fraction.

Answer»

5.6

Now write the given decimal without the decimal point as the numerator of the fraction.

In the denominator, write 1 followed by as many zeros as there are decimal places in the given decimal.

Then we have,

= 5.6 = (56/10)

Now reduce the above fraction to the simplest form.

= (56/10) … [÷ by 2]

= (28/5)

= [5(3/5)]

96.

Fill in the blanks to make the statement true.5 rupees 5 paise = ₹________.

Answer»

5 rupees 5 paise = ₹ 5.05

97.

Write each of the following as decimals:-(a) 88/10(b) 2/10(c) 3/2(d) 2/5

Answer»

(a) 88/10

= 80/10 + 8/10

= 8 + 0.8 = 8.8

(b) 2/10

= 4 + 2/10

= 4 + 0.2 = 4.2

(c) 3/2 = (2 + 1)/2

= 2/2 + 1/2

= 1 + 0.5 = 1.5

(d) 2/5 = 0.4

98.

Nasreen bought 3 m 20 cm cloth for her shirt and 2 m 5 cm cloth for her trouser. Find the total length of cloth bought by her

Answer» Length of cloth bought for Nasreen shirt = 3m 20cm` = 3m+20/100m = 3.2m`
Length of cloth bought for Nasreen trouser = 2m 5cm `= 2m+5/100m = 2.05m`
So, total lenght of cloth bought by Nasreen `=3.2+2.05 = 5.25m = 5m 25cm`
99.

Urmila’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 by bus. How much distance does she travel by bus?

Answer» Total distance=5.350 km
distance traveled by on foot=1.070 km
distance travelled by bus=total distance traveled - distance travelled by on foot
=5.35-1.07
=4.28 km.
100.

Express as km using decimals.(a) 8 m(b) 88 m(c) 8888 m(d) 70 km 5 m

Answer»

(a) 8 m = 8/1000 = 0.008 km

(b) 88 m = 88/1000 = 8.888 km

(c) 8888 m = 8888/1000 km = 8.888 km

(d) 70 km 5 m = (70 + 5/1000) km = 70.005 km