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

        Sol. (I) 31. 0040                          (II)    13.0000

                     -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+? =9318.78

(II)               ? -7328.96 = 5169.38

(I)                 Let   5172.49 + 378.352+? =9318.78

Then, X = 9318.678 – (5172.49) = 9318.678 – 5550.842 = 3767. 836,

(II)               Let X – 7328.96 =5169.38. then, X = 5169,38 + 7328.38 + 7328.96 = 12498.34.

Ex. 7.  Find the products: (I) 6.3204 x 100

      Sol. (I) 6.3204 x 200 = 100 = 632.04.

     (II).069 x 10000 = 0690 x 10000 = 690.

Ex. 8. Find the products

(I)                 2.61 X 1.3   (II) 2.1693 x 1.4   (III) .4x.04 x .004 x 40.

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

 2.61 x 1.3 = 3.393.

        (II) 21693 x 14 = 303702. Sum of decimal places = ( 4+ 1) =5.

                2.1693 x 1.4 = 3.03702.

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

               4 X 04 x .004 x 40 = 002560.

Ex.9. given that 268 x 74 = 19832, find the value of 2.68 x .74.

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

         2.68 x 74 = 1.9832.

Ex. 10. Find the quotient:

       (I) 0.63 /9           (II) 0.0204 /17         (III) 3. 1603 /13.

 Sol.10.. (I) 63 / 9 = 7. Dividend contains 2 places of decimal.

            0.63 / 9= 0.7.

         (II)          204 / 17 = 12. Dividend contains 4 places of decimal o.0204 / 17 = 0012.

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

          3.1603 /13 =2431.