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我们知道,整数和分数统称有理数.即所有分数都是有理数,那么所有小数呢?下面我们首先来谈谈分数与小数的关系.所有分数都能化成小数,一个最简分数,当分母不含2和5以外的质因数时,一定能化成有限小数,否则,就只能化成无限小数,并且一定是循环小数.例如17化成小数,必定是循环小数,1除以7,至多商到小数点后第7位,就必定会出现“循环”,这是因为除数是7所得的余数是1～6(不是0,否则结果是有限小数)之一,反之,是不是所有的小数也都能化成分数呢?
We know that integers and fractions are collectively known as rational numbers. That is, all fractions are rational numbers. So all the decimals? Let’s talk about the relationship between fractions and decimals. All fractions can be reduced to decimals, a simplest fraction when the denominator does not contain 2 When the prime factor is other than 5, it must be reduced to a finite decimal number. Otherwise, it can only be converted into an infinite decimal, and it must be a decimal. For example, 17 is converted into a decimal, it must be a decimal, 1 is divided by 7, and at most trades to the decimal point. 7-bit, there will be a “circular”, because the remainder when the divisor is 7 is 1 to 6 (not 0, otherwise the result is a finite decimal). Conversely, can all fractions be converted into fractions? ?