Example-5.

  1. Using the above theorems, without actual division, state whether decimal form of the following rational numbers are terminating or non-terminating, repeating decimals (i) 16/ 125 (ii) 25/ 32 (iii) 100/ 81 (iv) 41/ 75

    Solution :

     (i) 16 /125=16/ ×5×5× ×5=16/5 has a has a terminating decimal form.

    (ii)25/32=25/ ×2×2×2×2×2=25/25 has a terminating decimal form.

    (iii)100/81= 100/×3×3×3×3=100/34 has a non-terminating, repeating decimal form

    (iv)41/75=41/×3×5×5=41/×3×52 has a non-terminating, repeating decimal form.

    Example-6.

     Write the decimal form of the following rational numbers without actual division

    (i)35/50     (ii)21/25     (iii)7/8

    solution:

     (i)35/50=7×5/×2×5×5=7/×2×5=7/101=0.7

    (ii)21/25=21/×5×5= 21×22/×5×5×22=21×4/52×22=84/102=0.84,

    (iii)7/8=7/2×2×2=7/23=7×53/(23×53)=7×125/(2×5)3=875/(10)3=0.875

    EXERCISE- 1.3


    1.Write the following rational numbers in their decimal form and also state which are terminating and which are non-terminating, repeating decimal form.

    (i) 3/8     (ii)229/400     (iii)41/5   (iv)2/11   (v)8/125

    2.Without performing division, state whether the following rational numbers will have a terminating decimal form or a non-terminating, repeating decimal form.

    (i)13/3125    (ii)11/12    (iii)64/455    (iv)15/1600    (v)29/343    (vi)23/23.52    (vii)129/22.57.75    (viii)9/15    (ix) 36/100    (x)77/210



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