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【OG20-P289-410题】
If r and s are positive integers, can the fraction r/s be expressed as a decimal with only a finite number of nonzero digits?
(1) s is a factor of 100.
(2) r is a factor of 100.
分析A选项
分析B选项
分析C选项
分析D选项
分析E选项
要使r/s可以化成有限小数,就意味着,可以把分母化为10的倍数。因为每一个有限小数都可以写成n*10^-a的形式。而如果要把分母化成10的倍数就意味着要么分子和分母可以约掉2和5以外的其他质数,要么,就只含有2或5这两个因子。
条件一说s是100的因子,那么s当中就只能含有2或5这两个因子,所以充分
条件二说r是100的因子,但由于s不确定,例如r=5,s=3,此时就是无限小数;r=5,s=2,此时就是有限小数,所以仅凭条件一,无法判断。
所以选A
247789pvpc
是不是我把题目意思理解错了?比如条件1 s=2, 假如r也等于2,那么就是1.0,小数位是含0的呀,不就不符合条件了吗?
龙城飞将回复 247789pvpc
我做的时候也是这么想的,并且一开始以为答案是把整数都看作符合条件的小数了,后来查了一下题干中decimal以及fraction的含义,才发现这里不应该考虑整数:
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2022-11-30 14:26:35
龙城飞将回复 龙城飞将
decimal:【牛津】a fraction (= a number less than one) that is shown as a dot or point followed by the number of tenths, hundredths, etc. 小数 ------ fraction:【新牛津】a numerical quantity that is not a whole number. 意思是fraction一般不当做整数来考虑,至于fraction是否必须小于1,我持怀疑态度,毕竟5/3这样的分数比比皆是。但是就“fraction不能是整数”这一点而言,我觉得还是有信服度的。
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2022-11-30 14:34:10
499685skw
因数含有2或5的最终都可以得到一个有限小数
nishiki
一个分数的分母只要是100的因子,这个分数就可以写成a/100的形式, 就一定是有限小数
637298zxft
非零数位有限 没说不让你有0,比如0.02中非0位是2 只有一个2 他是有限的 没说不让你有0,0.00002也没问题
冲他丫的
非零数位是有限的小数 条件1 被除数是1/2/5才有用
贾思敏
定理:分母含有2、5的,一定是有限小数 要使得r/s是be expressed as a decimal with only a finite number of nonzero digits(有限小数),s一定要含有2或5或2和5。 条件一:s是100的因子,就是分母s含有2和5,那么r/s是有限小数,充分。 条件二:只知道r是100的因子,未知s是否含有2或5或2和5,不充分。
目标750
题干:r/s能不能除尽?; ;条件1:分母s是100的因子,(定理-所有数里面分母含有2或5,一定是有限小数),充分; ;条件2:分子r是100的因子,能否除尽取决于分母,不取决于分子,不充分;
171570aaqd
非零数位是有限的 小数
你这只猪
做对了却选错了,眼瞎了,彻底无语
一心只想杀鸡
题目说的是 can the fraction r/s be expressed as a...问的是有没有可能,主要有可能有是充分的条件
一心只想杀鸡回复一心只想杀鸡
只要
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2020-05-21 11:38:15
KUSO_
所以整数也可以用小数来表示?
212629sr
1/100=0.01 小数里不是带有0吗?
你这只猪回复212629sr
你应该是理解错了吧
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2020-06-08 16:04:50
321868ffjp回复212629sr
同问,如果r=1,s=100,0.01不就有0le ma
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2020-07-22 23:01:03
Junwei
R/S....看反了
374729so
With ONLY a finite number of nonzero digits ----只含有限个(不能是无限个)非零数字
HazelKwo
查了半天说decimal不包括integer。当s=1时,r/s=r为integer,不就是条件1的特例吗?题目不是要求expressed as a decimal吗?
jadexia回复HazelKwo
我也错在这里,如果是r/s=100/10 = 10, 就不是decimal了。。。
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2019-10-31 18:25:11
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