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 EXAMPLES SOLVED EXAMPLES:

Ex.1. convert the following into vulgar fractions:

(I)                 0.75

(II)               3.004

(III)             .006.

                           Sol. (I) 0.75 = 75/100=3/4

                                  (II) 3.004 = 3004/1000 751/250.

        (IV)             . 0056 = 56/10000 =7/1250.

Ex.2. arrange the fractions 5/8, 7/12, 13/16, 16/ 29 and 3/5 in ascending order of magnitude.

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

           5/8 = 0.625, 7/12 = 0. 5833, 13/16 =0. 81125, 16/29 = 0. 5517 and 3/4 = 0. 75

           Now, 0.5517 <0. 5825 < 0. 75 < 0. 8125.

         16/29 < 7/ 12 < 5/8 < 3/4 < 13/16.

Ex. 3.  Arrange the fractions 3/5, 4/7, 8/9 and 9/11 in their descending order.

         Sol.  Clearly, 3/5 = 0.6, 4/7 = 0.571, 8/9 = 0.88, 9/11 = 0.818.

          Now, 0.88> 0.818 > 0.6 > 0. 571.

         8/9 > 9>11 > 3/5 >4/7.

Ex. 4. Evaluate: (I) 6202. 5 + 620. 25 + 62. 025 + 6. 2025 + 0.62025

                       (II) 5. 064 + 3. 98 + .7035 + 7.6 + .3+ 2.

Sol> (I)   6202.5                                                   (II) 5. 064

                  620.25                                                        3.98

                       62.025                                                   0. 7036

                          6.2025                                                 7.6

                       + 0.62025                                               2.0

                     6891.59775                                            19.6476

Ex.5.. Evaluate: (i) 31.004 – 17.2386