纯循环小数循环节的规律

Recurring Period of Pure Recurring Decimal

纯循环小数循环节的规律是 :ab a,b是自然数 ,a<b,( a,b) =1能表示成纯循环小数的充要条件是 ( b,10 ) =1,且对满足上述条件的任意小于 b的自然数 a,ab化成小数时循环节节长都是相同的 .进一步得到了对任意自然数 b ( b,10 ) =1。

a/b (a and b are natural numbers; a<b, (a, b) = 1) can be expressed as pure recurring decimal if and only if (b, 10) = 1. The recurring period of decimal a/b, where a<b, is always the same. The law of the length of decimal a/b when natural number b ((b, 10) = 1) is obtained.