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[개념 기사] [가이드] 빙글빙글 도는 순환소수
최지원 기자♬ 2020.02.28 01:35

 

 

 

안녕, 여러분! 나는 순환소수라고 해. 순환소수가 뭐냐고? 다들 서울 지하철 노선도를 보고, 2호선만이 가진 특징을 찾아볼래?

 

벌써 찾은 친구들도 있는 것 같은데~. 이 특징이 나를 이해하는 핵심 키워드야!

 

 

2호선의 특징은 순환선이라는 거야!

다른 노선을 보면 시작과 끝이 정해져 있지만, 2호선은 하나로 이어져 있어 시작과 끝을 알 수 없어. 이렇게 계속 도는 걸 ‘순환’이라고 해.

 

 

순환하는 2호선. 시작과 끝을 알 수 없다.

 

 

자, 이제 우리 가족을 소개해볼까? 우리 가족은 엄마, 아빠, 나, 그리고 우리 누나 이렇게 네 명이야.

우리 엄마는 ‘분수’, 우리 아빠는 ‘소수’지. 분수는 전체에 대한 부분을 나타내는 수의 표기법인데, 위에 있는 분자를 아래에 있는 분모로 나눠서 나타내면 소수가 돼.

 

 

나와 우리 누나는 엄마와 같이 있을 때는 문제가 없는데, 아빠와 함께 있으면 항상 문제가 생겨.

누나는 내가 엄마랑 있을 때는 조용한데, 아빠랑 있으면 같은 말을 너무 많이 한대. 내가 아빠를 따라해 소수 형태일 땐 말이 좀 길어지거든.

 

 

항상 똑 부러진 누나는 같은 분수지만 분자를 분모로 나누면 소수점 아래의 숫자가 몇 개인지 셀 수 있어.

예를 들어 310, 34을 소수로 나타내면 0.3, 0.75로 딱 떨어지지? 그런데 나는 누나와는 달라. 소수점 아래에 숫자가 몇 개인지 셀 수 없는 모양이지. 

 

13을 소수로 고치면 0.333333…으로 3이 계속 반복되는 구조지? 또 411는 0.36363636…으로 3과 6이 계속 반복돼.

이때 반복되는 숫자를 ‘순환마디’라고 불러. 13은 순환마디가 1개지만, 17은 0.142857 142857…로 순환마디가 6개나 돼.

 

 

순환마디가 너무 길면 어떡하냐고? 걱정마. 순환마디의 개수는 분모의 수보다 커질 수 없거든. 예를 들어 17의 순환마디는 최대 6개, 111은 최대 10개야. 그 이유는 7로 나눌 때 나올 수 있는 나머지는 1, 2, 3, 4, 5, 6으로 6개밖에 없기 때문이야.

 

이제 나에 대해서 좀 이해하게 됐니? 나도 말을 반복하는 게 힘들지만, 어쩌겠어 이게 나인 걸.

여러분도 나를 만나면 너무 어렵다 생각하지 말고, 따뜻하게 다가와 주길 바라~!

 

※오늘의 퀴즈

9/35는 순환소수일까요?

1. 그렇다

2. 아니다

 

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