Recurring Decimals (or Repeating Decimals)

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Recurring Decimals (or Repeating Decimals)1. Recurring DecimalIf a figure or a set of figures is repeated continuously in a decimal fraction, it is called a recurring decimal (also known as repeating decimal and circulating decimal).

A repeating decimal is denoted by placing a horizontal line above the repeated numerals. Another way to denote a recurring decimal is placing dots over the first and last digits.

Examples

(a) 13=0.333... = 0.3¯ = 0.3˙

(b) 17=0.142857142857142857...  = 0.142857¯ = 0.1˙42857˙

(c) 712=0.58333...  = 0.583¯ = 0.583˙
2. Type of Recurring DecimalsRecurring Decimals can be classified into two categories - Pure Recurring Decimals and Mixed Recurring Decimals
(i) Pure Recurring DecimalsPure Recurring Decimal is a decimal fraction in which all the figures after the decimal point are repeated.

Examples

(a) 13=0.333... = 0.3¯ = 0.3˙

(b) 411=0.36363636... = 0.36¯ = 0.3˙6˙
(ii) Mixed Recurring DecimalsMixed Recurring Decimal is a decimal fraction in which some figures are not repeated and some figures are repeated.

Examples

(a) 712=0.58333...  = 0.583¯ = 0.583˙

(b) 8766=1.3181818...  

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