Ex. 1. Convert the following into vulgar fraction:

            (i) 0.75             (ii) 3.004          (iii)  0.0056

Sol. (i). 0.75 = 75/100 = 3/4    (ii) 3.004 = 3004/1000 = 751/250    (iii) 0.0056 = 56/10000 = 7/1250

Ex. 2. Arrange the fractions 5/8, 7/12, 13/16, 16/29 and 3/4 in ascending order of magnitude.

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

        5/8 = 0.624, 7/12 = 0.8125, 16/29 = 0.5517, and 3/4 = 0.75

        Now, 0.5517<0.5833<0.625<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, 9/111 = 0.818.

        Now, 0.88 > 0.818 > 0.6 > 0.571

        \ 8/9 > 9/11 > 3/4 > 13/ 16

Ex. 4. Evaluate : (i) 6202.5 + 620.25 + 62.025 + 6.2025 + 0.62025

                             (ii) 5.064 + 3.98 + 0.7036 + 7.6 + 0.3 + 2

Sol.  (i)  6202.5                                                    (ii)  5.064

                620.25                                                         3.98

                  62.025                                                       0.7036

                    6.2025                                                     7.6

           + __  0.62025                                                   0.3

              6891.59775                                                 _2.0___

                                                                                  19.6476

Ex. 5. Evaluate : (i) 31.004 – 17.2368                       (ii) 13 – 5.1967

Sol.  (i)    31.0040                                                       (ii)   31.0000

             – 17.2386                                                            – _5.1967  

13.7654                                                                                                                                  7.8033  

Ex. 6. What value will replace the question mark in the following equations ?

(i)                 5172.49 + 378.352 + ? = 9318.678

(ii)               ? – 7328.96 + 5169.38

Sol.  (i) Let       5172.49 + 378.352 + x = 9318.678

                        Then , x = 9318.678 – (5172.49 + 378.352) = 9318.678 – 5550.842 = 3767.836

        (ii) Let      x – 7328.96 = 5169.38. Then, x = 5169.38 + 7328.96 = 12498.34.

Ex. 7. Find the products: (i) 6.3204 * 100               (ii) 0.069 * 10000

Sol.  (i) 6.3204 * 1000 = 632.04                     (ii) 0.069  * 10000 = 0.0690 * 10000 = 690

Ex. 8. Find the product:

            (i) 2.61 * 1.3                (ii) 2.1693 * 1.4           (iii) 0.4 * 0.04 * 0.004 * 40

Sol.  (i) 261 8 13 = 3393. Sum of decimal places of given numbers = (2+1) = 3.

             2.61 * 1.3 = 3.393.

        (ii) 21693 * 14 = 303702. Sum of decimal places = (4+1) = 5

              2.1693 * 1.4 = 3.03702.

       (iii) 4 * 4 * 4 * 40 = 2560. Sum of decimal places = (1 + 2+ 3) = 6

              0.4 * 0.04 * 0.004 * 40 = 0.002560.

Ex. 9. Given that 268 * 74 = 19832, find the values of 2.68 * 0.74.

Sol.  Sum of decimal places = (2 + 2) = 4

         2.68 * 0.74 = 1.9832.

Ex. 10. Find the quotient:

            (i) 0.63 / 9                    (ii) 0.0204 / 17                         (iii) 3.1603 / 13           

Sol.  (i) 63 / 9 = 7. Dividend contains 2 places decimal.

             0.63 / 9 = 0.7.

        (ii) 204 / 17 = 12. Dividend contains 4 places of decimal.

              0.2040 / 17  = 0.0012.

        (iii) 31603 / 13 = 2431. Dividend contains 4 places of decimal.

               3.1603 / 13 = 0.2431.

Ex. 11. Evaluate :

            (i) 35 + 0.07                            (ii) 2.5 + 0.0005

(iii)             136.09 + 43.9

Sol. (i) 35/0.07 = ( 35*100) / (0.07*100) = (3500 / 7) = 500

      (ii) 25/0.0005 = (25*10000) / (0.0005*10000) = 25000 / 5 = 5000

     (iii) 136.09/43.9 = (136.09*10) / (43.9*10) = 1360.9 / 439 = 3.1

Ex. 12. What value will come in place of question mark in the following equation?

            (i) 0.006 +? = 0.6                    (ii) ? + 0.025 = 80

Sol.  (i) Let 0.006 / x = 0.6, Then, x = (0.006 / 0.6) = (0.006*10) / (0.6*10) = 0.06/6 = 0.01

        (ii) Let x / 0.025 = 80, Then, x = 80 * 0.025 = 2

Ex. 13. If (1 / 3.718) = 0.2689, Then find the value of (1 / 0.0003718).

Sol.  (1 / 0.0003718 ) = ( 10000 / 3.718 ) =  10000 * (1 / 3.718) = 10000 * 0.2689 = 2689.

                                                                                       ___                ______                  

Ex. 14. Express as vulgar fractions : (i) 0.37    (ii) 0.053     (iii)  3.142857

                __                                                  ___

Sol. (i)  0.37 = 37 / 99 .                       (ii)  0.053 = 53 / 999

                  ______             ______ 

        (iii) 3.142857 = 3 + 0.142857 = 3 + (142857 / 999999) = 3 (142857/999999)

                                                                        _                       __                      _

Ex. 15. Express as vulgar fractions : (i) 0.17           (ii) 0.1254        (iii)  2.536

                _

Sol. (i) 0.17 = (17 – 1)/90 = 16 / 90 =  8/ 45

                    __

       (ii) 0.1254 = (1254 – 12 )/ 9900 = 1242 / 9900 = 69 / 550

      (iii)  2.536 = 2 + 0.536 = 2 + (536 – 53)/900 = 2 + (483/900) = 2 + (161/300) = 2 (161/300)

Ex. 16. Simplify:  0.05 * 0.05 * 0.05 + 0.04 * 0.04 * 0.04

                               0.05 * 0.05 – 0.05 * 0.04 + 0.04 * 0.04

Sol. Given expression  = (a³ + b³) / (a² – ab + b²), where a = 0.05 , b = 0.04

                                     = (a +b ) = (0.05 +0.04 ) =0.09