有一初一数学题(请将问题看完)(1)将下列小数化成分数形式 0.431(431循环) 0.6528(28循环) 0.43

hddjh2022-10-04 11:39:541条回答

有一初一数学题(请将问题看完)
(1)将下列小数化成分数形式
0.431(431循环) 0.6528(28循环)
0.431因为没有不循环的部分所以直接将431当做分子,加上分母999(3个9)和分数线就成了与原小数相同值的分数.
0.6528因为有两个不循环的小数部分和两个循环的小数部分,所以直接减去不循环的小数部分(65)做分子再加上分母9900和分数线就成了与原小数相同值的分数.
问题是这些都是答案,可并没有解释清楚为什么会这样,我想做到触类旁通,哪位高手能解答?快啊.拜托拜托,千万千万要快!悬赏我一分都不会少,拜托了!

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kongkong987662 共回答了17个问题 | 采纳率94.1%
因为0.431(431循环)相当于是431*0.001(001循环),而0.001(001循环)恰好等于1/999,因此相当于是431*1/999=431/999
分母的9的个数取决于循环部分的数字个数,例如0.31(31循环)就应该取分子为99.这是因为对于0.00……01(00……01循环)而言它恰好等于1/99……99,所以所有类似的循环小数都可以这样处理.
如果有不循环的部分,如0.6528(28循环),可化为0.6528(28循环)=1/100*65.28(28循环),这样就没有不循环的小数部分了.对它的小数同上处理,分母应该是99,再除以前面的100,就成了9900.
1年前

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