RD Sharma 2020 2021 Solutions for Class 6 Maths Chapter 7 - Decimals

Answer:

(i) $525 + \frac{40}{100}$ = 525.40
(ii) $12 + \frac{35}{1000}$ = 12.035
(iii) $15 + \frac{17}{1000}$ = 15.017
(iv) $88 + \frac{48}{100}$ = 88.48

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.

Answer:

(i) We have 8 hundredths.
Therefore, the decimal is 0.08.

(ii) In its lowest form, the fraction is $\frac{3}{10}$.
We have 3 tenths.
Therefore, the decimal is 0.3.

(iii) We have eighteen thousandths.
Therefore, the decimal is 0.018.

(iv) $\frac{208}{100} = \frac{200}{100} + \frac{8}{100} = 2 + \frac{8}{100}$
We have 2 and 8 hundredths.
Therefore, the decimal is 2.08.

(v)$\frac{888}{1000} = \frac{800}{1000} + \frac{80}{1000} + \frac{8}{1000} = \frac{8}{10} + \frac{8}{100} + \frac{8}{1000}$
We have 8 tenths, 8 hundredths and 8 thousandths.
Therefore, the decimal is 0.888.

Answer:

(i) $12\frac{1}{4} = 12 + \frac{1}{4}$
= $12 + \frac{25}{4\times 25} = 12 + \frac{25}{100}= 12.25$

(ii) $7\frac{1}{8} = 7 + \frac{1}{8}$

$7 + \frac{1\times 125}{8\times 125} = 7 + \frac{125}{1000} = 7.125$

(iii) $5\frac{1}{20} = 5 + \frac{1}{20}$
$= 5 + \frac{1\times 5}{20\times 5} = 5 + \frac{5}{100} = 5.05$

Answer:

(i) 0.04
  =0 + 0.04
  = 0 + 4 hundredths
  = $0 + \frac{4}{100}$
  = $\frac{4}{100}$
  = $\frac{1}{25}$

(ii) 2.34
   = 2 + 0.34
   = 2 + 34 hundredths
   = 2 + $\frac{34}{100}$
   = $\frac{2\times 100}{100} + \frac{34}{100}$
   = $\frac{200}{100} + \frac{34}{100}$
   = $\frac{234}{100}$
   = $\frac{117}{50}$

(iii) 0.342
     = 0 + 342 thousandths
     = $\frac{342}{1000}$
     = $\frac{171}{500}$

(iv) 1.20
    = 1 + 0.20
    = 1 + 20 hundredths
    = 1 + $\frac{20}{100}$
    = $\frac{100}{100} + \frac{20}{100}$
    = $\frac{120}{100}$
    = $\frac{6}{5}$

(v) 17.38
    = 17 + 0.38
    = 17 + 38 hundredths
    = 17 + $\frac{38}{100}$
    = $\frac{17\times 100}{100} + \frac{38}{100}$
    = $\frac{1700}{100} + \frac{38}{100}$
    = $\frac{1738}{100}$
    = $\frac{869}{50}$

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.

Answer:

(i) $\frac{23}{10} = \frac{20 + 3}{10} = \frac{20}{10} + \frac{3}{10} = 2 + \frac{3}{10}$ = 2.3

(ii) $\frac{139}{100} = \frac{100+30+9}{100} = \frac{100}{100} + \frac{30}{100} + \frac{9}{100} = 1 + \frac{3}{10} + \frac{9}{100}$ = 1.39

(iii) $\frac{4375}{1000}= \frac{4000+300+70+5}{1000} = \frac{4000}{1000} + \frac{300}{1000} + \frac{70}{1000} + \frac{5}{1000}= 4 + \frac{3}{10} + \frac{7}{100} + \frac{5}{1000}$ = 4.375

(iv) $12\frac{1}{2} = 12 + \frac{1}{2}$= $12 + \frac{1\times 5}{2\times 5}$ = $12 + \frac{5}{10}$ = 12.5

(v) $75\frac{1}{4} = 75 + \frac{1}{4}$$= 75 + \frac{1\times 25}{4\times 25} = 75 + \frac{25}{100} = 75.25$

(vi) $25\frac{1}{8} = 25 + \frac{1}{8}$ = $25 + \frac{1\times 125}{8\times 125} = 25 + \frac{125}{1000} = 25.125$

(vii) $18\frac{3}{24} = 18 + \frac{3}{24} = 18 + \frac{1}{8} = 18 + \frac{125\times 1}{125\times 8} = 18 +\frac{125}{1000} = 18.125$

(viii) $39\frac{7}{35 } = 39 + \frac{7}{35} = 39 + \frac{1}{5} = 39 + \frac{1\times 2}{5\times 2} = 39 + \frac{2}{10} = 39.2$

(ix) $15\frac{1}{25} = 15 + \frac{1}{25} = 15 + \frac{1\times 4}{25\times 4} = 15 + \frac{4}{100} = 15.04$

(x) $\frac{111}{250} = \frac{111\times 4}{250\times 4} = \frac{444}{1000} = 0.444$

Answer:

(i) $0.5 = \frac{5}{10} = \frac{1}{2}$
(ii) $2.5 = \frac{25}{10} = \frac{5}{2}$
(iii) $0.60 = \frac{60}{100} = \frac{3}{5}$

(iv) $0.18 = \frac{18}{100} = \frac{9}{50}$

(v) $5.25 = \frac{525}{100} = \frac{21}{4}$

(vi) $7.125 = \frac{7125}{1000} = \frac{57}{8}$

(vii) $15.004 = \frac{15004}{1000} = \frac{3751}{250}$

(viii) $20.375 = \frac{20375}{1000} = \frac{163}{8}$

(ix) $600.75 = \frac{60075}{100} = \frac{2403}{4}$
(x) $59.48 = \frac{5948}{100} =\frac{1487}{25}$

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.

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.

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.
2 rupees and 60 paisa = $2 + \frac{60}{100}$
= Rs 2.60

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

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.
4 cm 5 mm = $4 + \frac{5}{10}$
                  = 4.5 cm

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 = $15 + \frac{35}{1000}$
                   =15.035 km

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.
5 kg 750 g = $5 + \frac{750}{1000}$
                 =5.750 kg

(v) 36 kg 50 g
We know that 1000 g = 1 kg.
Therefore, 1 g = 1/1000= 0.001 kg.
36 kg 50 g = $36 + \frac{50}{1000}$
                = 36.050 kg

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
           = $5 + \frac{25}{100}$
           = Rs 5 and 25 paisa

(ii) 8.354 kg
We know that 1000 g = 1 kg.
So, 1 g = 1/1000 kg.
Therefore, 8.354 = 8+ 0.354
                    = $8 + \frac{354}{1000}$
                    = 8 kg 354 g

(iii) 3.5 cm
We know that 10 mm = 1 cm.
So, 1 mm = 1/10 cm.
Therefore, 3.5= 3+ 0.5
               = $3 + \frac{5}{10}$
               = 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

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.

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.

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.

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.

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

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

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

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

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

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

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.

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

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

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.

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

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

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

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.

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.

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

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

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

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.

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.

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.

Answer:

(a) 0.004
Since the denominator is 1000, we have to mark the decimal such that 4 is in the thousandth place.

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.

Answer:

(c) $\frac{5}{1000}$
5 is in the thousandth place.

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

Answer:

(a) 0.231

$\frac{231}{1000} = \frac{200+30+1}{1000} = \frac{200}{1000} + \frac{30}{1000} + \frac{1}{1000} = \frac{2}{10} + \frac{3}{100} + \frac{1}{1000}$
We have 2 tenths, 3 hundredths and 1 thousandth.
Therefore, the value of 231/1000 is 0.231.

Answer:

(c) 3.005

$3\frac{5}{1000} = 3 + \frac{5}{1000} = 3 + 0.005 = 3.005$

Answer:

(b) 0.12

$\frac{3}{25} = \frac{3\times 4}{25\times 4} = \frac{12}{100} = 0.12$

Answer:

(c) 2.04

$2\frac{1}{25} = 2 + \frac{1}{25} = 2 + \frac{1\times 4}{25\times 4} = 2 + \frac{4}{100} = 2 + 0.04 = 2.04$

Answer:

(c) 4.875

$4\frac{7}{8} = 4 + \frac{7}{8} = 4 + \frac{7\times 125}{8\times 125} = 4 + \frac{875}{1000} = 4 + 0.875 = 4.875$

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

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

Answer:

(b) 0.01 m

We know that 100 cm = 1 m.
Therefore, 1 cm = 1/100 m = 0.01 m.

Answer:

(c) 0.001 km

We  know that 1000 m = 1 km.
Therefore, 1 m = 1/1000 m = 0.001 km.

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

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

Answer:

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

Answer:

(b) 5.555

Answer:

(c) 0.315
 
   0.350
− 0.035
=0.315

Answer:

(a) 1.545
2.5 + 3.05 − 4.005
= 5.55 − 4.005
= 1.545

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.

Answer:

The fraction $\frac{9}{10}$ in decimal form is 0.9

Hence, the correct option is (d).

Answer:

The fraction $\frac{7}{100}$ in decimal form is 0.07.

Hence, the correct option is (d).

Answer:

The fraction $\frac{3}{1000}$ in decimal form is 0.003.

Hence, the correct option is (c).

Answer:

​The fraction $\frac{173}{1000}$ in decimal form is 0.173.

Hence, the correct option is (c).

Answer:

$$\begin{gathered} 2\frac{19}{100}=\frac{219}{100} \\ =\frac{200+19}{100} \\ =\frac{200}{100}+\frac{19}{100} \\ =2+0.19 \\ =2.19 \end{gathered}$$

Hence, the correct option is (a).

Answer:

$$\begin{gathered} 31.08=31+0.08 \\ =31+\frac{8}{100} \\ =31+\frac{8÷4}{100÷4} \\ =31+\frac{2}{25} \\ =31\frac{2}{25} \end{gathered}$$

Hence, the correct option is (b).

Answer:

$2+\frac{3}{10}+\frac{4}{100}=2+0.3+0.04=2.34$

Hence, the correct option is (c).

Answer:

$\frac{3}{100}+\frac{5}{10000}=0.03+0.0005=0.0305$

Hence, the correct option is (c).

Answer:

$\frac{5}{10}+\frac{3}{100}=0.5+0.03=0.53$

Hence, the correct option is (a).

Answer:

9.02 − 5.7 =

$$\begin{gathered} \stackrel{8}{\cancel{9}} . \stackrel{10}{\cancel{0}} 2 \\ \underline{-5 . 7 0 } \\ \underline{ 3 . 3 2 } \end{gathered}$$

∴ 9.02 − 5.7 = 3.32

Hence, the correct option is (a).

Answer:

$$\begin{gathered} 2\frac{9}{40}=2+\frac{9}{40} \\ =2+\frac{9\times 25}{40\times 25} \\ =2+\frac{225}{1000} \\ =2+0.225 \\ =2.225 \end{gathered}$$

Hence, the value of $2\frac{9}{40}$ into a decimal fraction is 2.225.

Answer:

(i)
 $$\begin{gathered} 0.025=\frac{025}{1000} \\ =\frac{25÷25}{1000÷25} \\ =\frac{1}{40} \end{gathered}$$

(ii)
$$\begin{gathered} 0.35=\frac{35}{100} \\ =\frac{35÷5}{100÷5} \\ =\frac{7}{20} \end{gathered}$$

(iii)
$$\begin{gathered} 0.075=\frac{075}{1000} \\ =\frac{75÷25}{1000÷25} \\ =\frac{3}{40} \end{gathered}$$

Answer:

Let the required number be x.

According to the question,

$$\begin{gathered} 18.5-x=6.2376 \\ \Rightarrow x=18.5-6.2376 \end{gathered}$$

         $$\begin{gathered} 1 8 . \stackrel{4}{\cancel{5}} \stackrel{9}{\cancel{0}} \stackrel{9}{\cancel{0}} \stackrel{10}{\cancel{0}} \\ \underline{- 6 . 2 3 7 6 } \\ \underline{ 1 2 . 2 6 2 4 } \end{gathered}$$

$\Rightarrow x=12.2624$

Hence, 12.2624 subtracted from 18.5 gives 6.2376.

Answer:

$0.52314=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{1}{10000}+\frac{4}{100000}$        ...(1)
$0.52313=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{1}{10000}+\frac{3}{100000}$        ...(2)
$0.53201=0+\frac{5}{10}+\frac{3}{100}+\frac{2}{1000}+\frac{0}{10000}+\frac{1}{100000}$        ...(3)
$0.52321=0+\frac{5}{10}+\frac{2}{100}+\frac{3}{1000}+\frac{2}{10000}+\frac{1}{100000}$        ...(4)

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

Answer:

(i)
 $$\begin{gathered} 2.3675=2+0.3675 \\ =2+\frac{3675}{10000} \\ =2+\frac{3675÷25}{10000÷25} \\ =2+\frac{147}{400} \\ =2\frac{147}{400} \\ =\frac{947}{400} \end{gathered}$$

(ii)
​ $$\begin{gathered} 54.26=54+0.26 \\ =54+\frac{26}{100} \\ =54+\frac{26÷2}{100÷2} \\ =54+\frac{13}{50} \\ =54\frac{13}{50} \\ =\frac{2713}{50} \end{gathered}$$

(iii)
​ $$\begin{gathered} 75.35=75+0.35 \\ =75+\frac{35}{100} \\ =75+\frac{35÷5}{100÷5} \\ =75+\frac{7}{20} \\ =75\frac{7}{20} \\ =\frac{1507}{20} \end{gathered}$$

(iv)
​ $$\begin{gathered} 0.7575=\frac{7575}{10000} \\ =\frac{7575÷25}{10000÷25} \\ =\frac{303}{400} \end{gathered}$$

Answer:

Let the required value be x.

According to the question,
27.354 + x = 52
⇒ x = 52 − 27.354

         $$\begin{gathered} \stackrel{4}{\cancel{5}} \stackrel{11}{\cancel{2}} . \stackrel{9}{\cancel{0}} \stackrel{9}{\cancel{0}} \stackrel{10}{\cancel{0}} \\ \underline{- 2 7 . 3 5 4 } \\ \underline{ 2 4 . 6 4 6 } \end{gathered}$$

⇒ x = 24.646

Hence, 24.646 should 27.354 be increased to get 52.

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
 $$\begin{gathered} 2 . \stackrel{1}{0} 5 \mathrm{m} \\ \underline{+ 3 . 3 5 \mathrm{m} } \\ \underline{ 5 . 4 0 \mathrm{m} } \end{gathered}$$

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

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

 $$\begin{gathered} 5 . \stackrel{1}{0} \stackrel{1}{7} 5 \mathrm{kg} \\ \underline{+ 3 . 4 6 5 \mathrm{kg} } \\ \underline{ 8 . 5 4 0 \mathrm{kg} } \end{gathered}$$

Now, the bag with these contents weighs 9 kg.

Therefore, the weight of empty bag is

$$\begin{gathered} \stackrel{8}{\cancel{9}} . \stackrel{9}{\cancel{0}} \stackrel{10}{\cancel{0}} 0 \mathrm{kg} \\ \underline{- 8 . 5 4 0 \mathrm{kg} } \\ \underline{ 0 . 4 6 0 \mathrm{kg} } \end{gathered}$$

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

Answer:

36.36 − 28.4237 − 9.78 + 7.7
= 36.36 + 7.7 − (28.4237 + 9.78)

     $$\begin{gathered} \stackrel{1}{3} \stackrel{1}{6} . 3 6 \\ \underline{+ 7 . 7 0 } \\ \underline{ 4 4 . 0 6 } \end{gathered}$$             $$\begin{gathered} \stackrel{1}{2} \stackrel{1}{8} . \stackrel{1}{4} 2 3 7 \\ \underline{+ 9 . 7 8 0 0 } \\ \underline{ 3 8 . 2 0 3 7 } \end{gathered}$$

= 44.06 − 38.2037

     $$\begin{gathered} \stackrel{3}{\cancel{4}} \stackrel{13}{\cancel{4}} . \stackrel{10}{\cancel{0}} \stackrel{5}{\cancel{6}} \stackrel{9}{\cancel{0}} \stackrel{10}{\cancel{0}} \\ \underline{- 3 8 . 2 0 3 7 } \\ \underline{ 0 5 . 8 5 6 3 } \end{gathered}$$

= 5.8563

Answer:

Let the required number be x.

According to the question,
3.56 + x = 23.018
⇒ x = 23.018 − 3.56

 $$\begin{gathered} \stackrel{1}{\cancel{2}} \stackrel{12}{\cancel{3}} . \stackrel{9}{\cancel{0}} \stackrel{11}{\cancel{1}} 8 \\ \underline{- 3 . 5 6 0 } \\ \underline{ 1 9 . 4 5 8 } \end{gathered}$$

⇒ x = 19.458

Hence, 19.458 when â€‹added to 3.56 gives 23.018.

Answer:

$\frac{34}{10000}=\frac{0034}{10000}=0.0034$

Thus, $\frac{34}{10000}=\underline{0.0034}$.

Answer:

1 km = 1000 m
$$\begin{gathered} \Rightarrow 1 \mathrm{m}=\frac{1}{1000}\mathrm{km} \\ \Rightarrow 1 \mathrm{m}=0.001 \mathrm{km} \end{gathered}$$

Thus, $1 \mathrm{m}=\underline{0.001} \mathrm{km}$

Answer:

1 kg = 1000 g
$\Rightarrow 1 \mathrm{g}=\frac{1}{1000}\mathrm{kg}$


$$\begin{gathered} 7 \mathrm{kg} 15 \mathrm{g}=7 \mathrm{kg} +\frac{15}{1000}\mathrm{kg} \\ =7 \mathrm{kg} + 0.015 \mathrm{kg} \\ =7.015 \mathrm{kg} \end{gathered}$$

Thus, $7 \mathrm{kg} 15 \mathrm{g}=\underline{7.015} \mathrm{kg}$​

Answer:

1 l = 1000 ml
$\Rightarrow 1 \mathrm{m}l=\frac{1}{1000}l$


$$\begin{gathered} 2 l 5 \mathrm{m}l=2 l+\frac{5}{1000}l \\ =2 l+ 0.005 l \\ =2.005 l \end{gathered}$$

Thus, $2 l 5 \mathrm{m}l=\underline{2.005} l$​​

Answer:

1 m = 100 cm
$\Rightarrow 1 \mathrm{cm}=\frac{1}{100}\mathrm{m}$

$$\begin{gathered} 2 \mathrm{m} 5 \mathrm{cm}=2 \mathrm{m}+\frac{5}{100}\mathrm{m} \\ =2 \mathrm{m}+0.05 \mathrm{m} \\ =2.05 \mathrm{m} \end{gathered}$$

Thus, $2 \mathrm{m} 5 \mathrm{cm}=\underline{2.05} \mathrm{m}$​​​.

Answer:

Answer:

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

(i)    307.12

(ii)   9543.025

(iii)  12.503

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

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.

Answer:

(i) 5 + $\frac{4}{10}$ = 5.4

(ii) 12 + $\frac{4}{100}$ = 12.04

(iii) 9 + $\frac{705}{1000}$ = 9.705

(iv) 0.526

(v) 47 + $\frac{6}{1000}$= 47.006

(vi) $\frac{8}{1000}$ =  0.008

(vii) 19 + $\frac{19}{100}$ = 19.19

Answer:

(i) $\frac{3}{10}$ = 0.3
(ii) 2 + $\frac{5}{10}$ = 2.5
(iii) 30 + $\frac{1}{10}$ = 30.1
(iv) 22 + $\frac{6}{10}$ = 22.6
(v) 100 + 2 + $\frac{3}{10}$ = 102.3

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.

Answer:

(i) $\frac{22}{10}$
Since the denominator is ten, the decimal is 2.2.

(ii)  3/2
Making the denominator 10, we have
3/2

= $\frac{3\times 5}{2\times 5}$
= $\frac{15}{10}$
= 1.5

(iii)  2/5
Making the denominator 10, we have
2/5
= $\frac{2\times 2}{5\times 2}$
= $\frac{4}{10}$
= 0.4

Answer:

(i) $40\frac{2}{5} = 40 + \frac{2}{5}$
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
 
= 40 + $\frac{2\times 2}{5\times 2}$
= 40 + $\frac{4}{10}$
= 40.4

(ii) $39\frac{2}{10 } = 39 + \frac{2}{10}$
Here, the denominator is 10.
Therefore, the decimal is 39.2.

(iii) $4\frac{3}{5} = 4 + \frac{3}{5}$
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
  
  = 4 + $\frac{3\times 2}{5\times 2}$
  = 4 + $\frac{6}{10}$
  =4.6

(iv)  $25\frac{1}{2}$ = 25 + $\frac{1}{2}$
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

   = $25 + \frac{1\times 5}{2\times 5}$
   = $25 + \frac{5}{10}$
   =25.5

Answer:

(i) 3.8
   = 3 + 8 tenths
   = 3 + $\frac{8}{10}$
   = $\frac{3\times 10}{10}$ + $\frac{8}{10}$ = $\frac{30}{10} + \frac{8}{10} = \frac{38}{10} = \frac{19}{5}$

(ii)  21.2
   = 21 + 2 tenths
   = 21 + $\frac{2}{10}$ = $\frac{21\times 10}{10} + \frac{2}{10} = \frac{210}{10} + \frac{2}{10} = \frac{212}{10} = \frac{106}{5}$

(iii) 6.4
    = 6 + 4 tenths
    = 6 + $\frac{4}{10}$
    = $\frac{6\times 10}{10} + \frac{4}{10} = \frac{60}{10} + \frac{4}{10} = \frac{64}{10} = \frac{32}{5}$

(iv)  1.0
Since the only number after the decimal is 0, the fraction is 1.

Answer:

(i)


(ii) 


(iii)


(iv)

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.

Answer:

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