PERIOD OF DECIMAL
In the decimal expansion of the rational numbers, the number of repeating decimals is called the length of the period of decimals.
(i) 25/4 = 3.571428571428......... has the length of the period of decimal = 6.
(ii) 27/110 = 3.4545......... has the length of the period of decimal = 2.
Express the rational number 1/27 in recurring decimal form by using the recurring decimal expansion of 1/3. Hence write 59/27 in recurring decimal form.
We know that 1/3 = 0.33..............
1/27 = (1/9) x (1/3)
1/27 = (1/9) x 0.33..............
1/27 = 0.037037..............
59/27 = 2 5/27
59/27 = 2 + 5/27
59/27 = 2 + (5 x 1/27)
59/27 = 2 + (5 x 0.037037..............)
59/27 = 2 + 0.185185..............
59/27 = 2.185185..............
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