DECIMAL FRACTIONS - EXERCISE 3 (SOLUTION 31 TO 40)

31.  2 x 5 = 10. Sum of decimal places = 4.

                    0.002 x 0.5 = 0.00010 = 0.001.

32.  1602 x 1 = 1602. Sum of decimal places = 5.

               16.02 x 0.5 = 0.0010 = 0.001.

33.  14 x 14 = 196. Sum of decimal places = 6.

                            0.0014 x 0.001 = 0.000196.

34.  4083 x 102 x 12 = 4997592. Sum o decimal places = 5.

                         40.83 x 1.02 x 1.2 = 49.97592.

35.  4 x 162 = 648. Sum of decimal places = 6.

                          0.04 x 0.0162 ==.000648 = 6.48 x 10⁻⁴

36.   3 x 3 x 3 x 3 x 30= 2430. Sum of decimal places = 6.

                      3 x 0.3 x 0.03 x 0.003 x 30 = 0.002430 = 0.00243.

37.  Sum of decimal places = 7.

                        Since the last digit to the extreme right will be zero (5 x 4 = 20), so there will be                                          6                 significant digits to the right of the decimal point.

38.   (.00625 of 23/6) = (625/100000 x 23/5) = 23/800.

39.  Given product = 0.3 x 0.25 x 0.5 x 0.125 x 24

                    = (3.10 x 25/100 x 5/10 x 125/1000 x 24) = 9/80 = 1/8

DECIMAL FRACTIONS - EXERCISE 3 (SOLUTION 21 TO 30)

21.  Given expression = (12.1212 + 17.0005) -9.1102 = (29.1217 – 9.1102) = 20.0115.

22.  Given expression = 892.7 – (573.07 +95.007) =892.7 – 668.077 = 224. 623.

23.  Let 3889 + 12.952 – X = 3854.002.

                   Then X = (3889 + 12.952) – 3854.002 = 3901.952 – 3854. 002 = 47.95.

24.    Let 138.009 + 341. 981 ) – 146.305=123.6 + X.

                     Then, X = (138.009 + 341.981) – (146.305 + 123.6)= 479.99 – 269.905 = 210.085.

25.  Let 832.58 – 242.31 = 779.84 –X .

                      Then, X = (779.84 + 242.31) – 832.58 = 1022.15 – 832.58 = 189.57.

26.  Let X + 542 + 5.43 = 603.26. then, X = 603.26 – (543 + 5.43 ) =603.26 – 548.43 = 54.83.

                         Missing digit = 8.

27.  3.14 x 10⁶ = 3.140000 x 1000000 = 3140000.

28.  518.000,000 = 5.18 x 100000000 = 5.18 x 10⁸.

29.  0.000006723 = 0.000006723 x 10⁶/10⁶ = 6.723 x 10⁻⁶.

30.  10 k = 0.001125/1.125 = 1.125/1125 = 1.125 x 10³/1125 x 10³ = 1/10³ = 10⁻³.

                      K=-3.

DECIMAL FRACTIONS - EXERCISE 3 (SOLUTION 11 TO 20)

1 1.      3/4 = 0.75, 5/6 = 0.833, 1/2 = 0.5, 2/3 = 0.66, 4/5 – 0.8, 9/10 – 0.9.

                         Clearly, 0.8 lies b between o.75 and 0.833.

                           4/5 lies between 3/4 and 5/6.

12.      7/8 = 0.975, 1/3 = 0.333, ¼ = 0.25, 23/24 = 0.958, 11/12 = 0.916 17/24 =0.708.

                             Clearly, 0.708 lies between 0.333 and 0.875.

                            17/24 lies between 1/3 and 7/8.

13.      4/5 = 0.8, 7/13 = 0.53, ½ = ½ = 0.5, 2/3 = 0.66, ¾ = 0.75, 5/7 = 0.714,

                  Clearly, 0.5 does not the between 0.53 and 0.8.

                  1/2 does not lie between 4/5 and 7/13.

14.      -7/10 = -0.7, 5/-8 = -5/8 = -0.625, 2/-3 = -2/3= -0.66.

                            Since – 0.7 < - 0.66< - 0.625, So -7/10 < 2/-3 < 5/-8.

15.       337.62

                               8.591

                            + 34.4

                             380.611

16.      1.0

                              0.1

                            0.01

                          0.001

 

                          1.111

 

17.           34.95

                      2240.016

                    +    23.98

                                   298.9446

18.      617.00

                                6.017

                                0.617

                              6.0017

                            629.6357

19.       48.950

                             

                              -    32.006

                                  16.944

20.      792.02

                        +101.32

                         893.34

                              893.34

 

               893.34

                       -  306.76

                        586.58

             

DECIMAL FRACTIONS - EXERCISE 3 (SOLUTION 1 TO 10)

1.      101 27/10000 = 101 + 27/100000=101 + 00027 = 101.00027

2.      0.36 = 36/100 = 9/25. Sum of numerator and denominator = 9 + 25 = 34

3.      Required decimal =1/60 x 60 = 1/3600 = .00027

4.      4 A + 7/B + 2 C + 5/D + 6 E = 47.2506

                      4 A + 7/B 2 C + 5/D + 6 E = 40+7 + 0.2 + 0.05 + 0.0006

                      Comparing the terms on both sides, we get:

                      4 A = 40, 7/B = 7, 2 C = 0.2, 5/D = 0.05, 6 e = 0.0006

                       (or) A = 10, b=1,C =0.1,D = 100, E=0.0001.

                      5 A + 3 B + 6 C + D + 3 E = (5 X 10) + ( 6 X 0.1) +  100 + (3 X 0.0001)

                     = 50 +3 + 0.6 + 100 + 0.0003 = 153.6003.

5.      converting each of the given fractions Into decimal form, we get:

                      1/3 =0.22, 2/5 = 0.4, 4/7 = 0.57, 3/5 = 0.6 = 5/6= 0.82, 6/7 = 0.857,

                      Clearly, 0.33 <0.4 < 0.57 <0.6 < 0.82<0.857 so, 1/3 <2/5<4/7<3/5<5/6<6/7.

6.      Converting each of the given fractions into decimal form, we get:

        2/3 = 0.66, 3/5 = 0.6, 7/9 = 0.77, 9/11 = 0.81, 8/9 = 0.88.

        Clearly, 0.6 <0.66 <0.77 <0.81.  So, 3/5 <2/3 <7/9 <9/11 < 8/9.

7.      Converting each of the given fractions into decimal form, we get:

                   5/9 = 0.55, 7/11 = 0.63, 8/15 = 0.533, 11/17 = 0.647.

                   Clearly, 0.647 > 0.63> 0.55> 0.533. So, 11/17 > 7/11> 5/9 >8>15.

8.       Converting each of the given fractions into decimal form, we get>

DECIMAL FRACTIONS - EXERCISE 3 (OBJECTIVE TYPE QUESTIONS 116 TO 119)

1.      The value of (0.1 x 0.1 x 0.1 + 0.02 0.02 x 0.02)/(0.2 x 0.2x 0.2+0.04 x 0.04 x0.04) is

a)      0.538

b)      5.38

c)      0.0538

d)      53.8

2.      The value of (0.96)³ - (0.1)³/(-.96)² + 0.096 + (0.1)² is:

a)      0.86

b)      0.95

c)      0.97

d)      1.06

3.      The value of (23)³ - .027/(2.3)² + .69 + .09 is :

a)      0

b)      1.6

c)      2

d)      3.4

4.      The value of (0.06) + (0.47)² + (0-.079)²/(0.006)² + (0.047)² + (0.0079)² is:

a)      0.1

b)      10

c)      100

d)      1000

                             ANSWERS

DECIMAL FRACTIONS - EXERCISE 3 (OBJECTIVE TYPE QUESTIONS 111 To 115)

111.       The value of (953 x .953 -.953 x .047 x .047)/(.953 x.953 x.953 x .953+.047x .047) is:

a)      .32

b)      .886

c)       1.1286

d)      None of these

112.       The value of (0.125 + 0.027)/(0.5 x 10.3 -0.09 -0.15) is:

a)      0.08

b)      0.2

c)       0.8

d)      1

113.       (10.3x 10.3 x10.3 +1)/10.3 x 10.3 -10.3 +1) is equal to:

a)      9.3

b)      10.3

c)       11.3

d)      12.3

114.       [8(3.75)³ + 1]/(7.5)² - 6.5] is equal to:

a)      9.5

b)      2.75

c)       4.75.

d)      8.5

115.       The value of (0.1 x0.1 x 0.1 +0.02 x 0.02 x 0.02 )/(0.2 x 0.2 x 0.2 + 0.04 x 0.04 

0.04x 0.04 x 0.04) is:

a)      0.0125

b)      0.125

c)       0.25

d)      0.5

ANSWERS 

DECIMAL FRACTIONS- EXERCISE 3 (OBJECTIVE TYPE QUESTIONS 106 TO 110)

 106.   The simplification of 0.2 x 0.2 + x 0.02 – 0.4 x 0.02 / 0.36 gives:

a)      0.009

b)      0.09

c)       0.9

d)      9

107.   The expression 11.98 x 11.98 + 0.02 x 0.02)will be a perfect square for X equal to:

a)      0.02

b)      0.2

c)       0.04

d)      0.4

108.   The value of (2.697 – 0.498)² + (2.697 + 0.498)²/2.697 x 2.697 + 0.498 x 0.498 is:

a)      0.5

b)      2

c)       2.199

d)      3.195

109.   The value of (0.137 + 0.098)² +(2.697 + 0.498)²/0.137 x 0.098 is:

a)      0.039

b)      0.235

c)       0.25

d)      4

110.   The value of (0.051 x 0.051 x 0.051 + 0.041 x 0.041 x 0.041)/0.051 x0.051 – 0.051 x 0.041 +0.041 x.047) is:

a)      0.00092

b)      0.0092

c)       0.092

d)      0.92
ANSWERS:

DECIMAL FRACTIONS = EXERCISE 3 (OBJECTIVE TYPE QUESTIONS 101 TO 105)

101.   (1.49 x 14.9 – 0.51 x 5.1 )

      (14.9 – 5.1) is equal to:

a)      0.20

b)      2.00

c)       20

d)      22

102.   4.2 x 4.2 – 1.9 x 1.9

     2.3 x 6.1                           =?

a)      0.5

b)      1

c)       1.9

d)      4.2

103.   Simplify: 5.32 x 56 + 5.32 x 44

                                                        (7.66)² - (2.34)²

a)      7.2

b)      8.5

c)       10

d)      12

104.   (0.6)⁴ - (0.5)⁴/(0.6)²+ (0.5)² is equal to:

a)      0.1

b)      0.11

c)       1.1

d)      11

105.   (7.5 x 7.5 + 37.5 + 2.5 x 2.5) is equal to:

a)      30

b)      60

c)       80

d)      100
ANSWERS

DECIMAL FRACTIONS- EXERCISE 3 (OBJECTIVE TYPE QUESTIONS 96 TO 100)

96.       The value of (68.237)² - (31.763)² is:

a)      3.6474

b)      36.474

c)       364.74

d)      3647.4

97.       Evaluate: (2.39)²  - (1.61)²

                 2.39 -1.61

a)      2

b)      4

c)       6

d)      8

98.       On simplification of (2.644)² - (2.356)²

                                             0.288                      , we get

a)      1

b)      4

c)       5

d)      6

99.       (36.54)² - (3.46)²

                                       ?

a)      3.308

b)      4

c)       33.08

d)      330.8

100.   The value of (67.542)² -(32.458)²

                         75.458 – 40.373

a)      1

b)      10

c)       100

d)      None of these


ANSWERS:

DECIMAL FRACTIONS - EXERCISE 3 (OBJECTIVE TYPE QUESTIONS 91 TO 95)

91.       5x 1.6 – 2 x 1.4 =?

1.3  

a)      0.47

b)      1.2

c)       1.4

d)      4

92.       The value of (4.7 x 13.26 + 4.7 x 9.43 + 4.7 x 77.31 ) is:

a)      0.47

b)      47

c)       470

d)      4700

93.       Simplify: 0.2 x 0.2 + 0.2 x 0.02

                                                    0.044  

a)      0.004

b)      0.4

c)       1

d)      2

94.       The value of (8.6 x 5.3 + 8.6 x 4.7)

                          (4.3 x 9.7 – 4.3 x 8.7)                           is:

a)      3.3

b)      6.847

c)       13.9

d)      20

95.       The value of (.896 x 5.3 + 8.6 x 4.7)

                        (.7x.0.64 + .7 x. 936)

a)      .976

b)      9.76

c)       1.28

d)      12.8

ANSWERS