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7.484848…, Classify the given number as rational or irrational. |
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Answer» Given decimal 7.484848... is a non-terminating recurring decimal. 7.4848....is a rational number. ********************************** The set of digits which repeats in non-terminating recurring decimal is CALLED period. The number of digits in a period of non-terminating decimal is called PERIODICITY . ************************************ In 7.484848..... Period = 48 Periodicity = 2 _____________________ Let x = 7.484848... ----( 1 ) MULTIPLY ( 1 ) with 100, we get 100x = 748.484848...---( 2 ) SUBTRACT ( 1 ) from ( 2 ) , we get 99x = 741 => x = 741/99 = 247/33 [ p/q form ] Therefore , 7.484848....= 247/33 is a rational number. •••••• |
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