锛堟媿澶ц吙锛夊搸锛佺湅鍒颁綔涓氭湰涓婂啓鐫€0.333...瑕佽浆鍖栨垚鍒嗘暟鏄笉鏄壒澶村ぇ锛熷埆鎱岋紝浠婂効鍜卞氨鐢ㄧ叜娉￠潰閮借兘鍚噦鐨勫ぇ鐧借瘽锛屾妸杩欎簨鍎挎暣鏄庣櫧锛佽寰楀垵涓偅浼氬効锛屾垜鐩潃鏁板鑰佸笀鏉夸功涓婄殑0.999...=1鐨勮瘉鏄庯紝涓嬪反閮藉揩鎺夊湴涓婁簡鈥斺€旇繖涓嶇瀛﹀晩锛佺幇鍦ㄦ墠鎳傦紝寰幆灏忔暟杞垎鏁板叾瀹炲氨鏄釜鎵捐寰嬬殑榄旀湳鎴忔硶銆?/p>

涓€銆佸厛鎼炴槑鐧藉暐鍙?寰幆灏忔暟"

涓句釜鏍楀瓙馃尠锛氫綘涔颁笁鏉ザ鑼惰姳浜?0鍧楅挶锛屽崟浠峰叾瀹炴槸3.333...鍏冨鍚э紵杩欑姘歌繙閲嶅鐨?灏辨槸鍏稿瀷鐨勨€?strong>鈥嬬函寰幆灏忔暟鈥?/strong>鈥嬨€傝鏄涓?.4121212...杩欑鍓嶅崐鎴笉寰幆銆佸悗鍗婃埅寰幆鐨勶紝鍜变滑鍙畠鈥?strong>鈥嬫贩寰幆灏忔暟鈥?/strong>鈥嬨€?/p>

鍏抽敭鐐硅鐗細

1. 鈥?strong>鈥嬪惊鐜妭鈥?/strong>鈥嬶細閲嶅鐨勯偅涓叉暟锛堟瘮濡?.727272...鐨勫惊鐜妭灏辨槸"72"锛?/li>
2. 鈥?strong>鈥嬫爣璁版硶鈥?/strong>鈥嬶細鍦ㄥ惊鐜妭棣栧熬鏁板瓧涓婄偣涓偣锛屾瘮濡?.3虈灏辨槸0.333...

浜屻€佷竾鑳借浆鍖栧洓閮ㄦ洸锛堟嬁0.636363...寮€鍒€锛?/h3>

鈥?strong>鈥嬬鈶犳锛氳鏈煡鏁扳€?/strong>鈥?br/> 鎺忓嚭绗斿啓锛氳x=0.636363...锛堣繖閲寈灏辨槸涓复鏃跺伐锛岀敤瀹屽氨鎵旓級

鈥?strong>鈥嬬鈶℃锛氭壘鍊嶆暟鍏崇郴鈥?/strong>鈥?br/> 鐪嬪惊鐜妭鏈夊嚑浣嶏紵杩欏効"63"鏄袱浣嶏紝閭ｅ氨缁檟涔?00锛?br/> 100x = 63.636363...锛堟敞鎰忥紒灏忔暟鐐瑰線鍙宠功浜嗕袱浣嶏級

鈥?strong>鈥嬬鈶㈡锛氱帺娑堟秷涔愨€?/strong>鈥?br/> 鎶婁袱寮忓瓙涓婁笅鐩稿噺锛?br/> 100x - x = 63.636363... - 0.636363...
鈫?br/> 99x = 63 锛堢濂囧惂锛熸棤闄愬惊鐜殑灏忓熬宸村叏娌′簡锛侊級

鈥?strong>鈥嬬鈶ｆ锛氭敹宸ュ緱鍒嗘暟鈥?/strong>鈥?br/> x = 63/99 = 7/11锛堝埆蹇樼害鍒嗭紒鍒嗗瓙鍒嗘瘝閮矫?锛?/p>

锛堟暡榛戞澘锛夐噸鐐瑰叕寮忥細鈥?strong>鈥嬪垎鏁?寰幆鑺傛暟瀛椕?10鈦?-1)鈥?/strong>鈥嬶紝n鏄惊鐜妭浣嶆暟銆傛瘮濡傚垰鎵嶇殑63梅(10虏-1)=63/99

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涓夈€佸疄鎴橈紒娣峰惊鐜皬鏁版€庝箞鐮达紵

鏉ラ亾鐪熼锛氭妸0.58333...鍖栨垚鍒嗘暟銆傝繖鏃跺€欏墠澶寸殑58涓嶅惊鐜紝鍚庡ご鐨?寰幆锛屽拫鏁达紵

鈥?strong>鈥嬫搷浣滄寚鍗楋細鈥?/strong>鈥?/p>

1. 鈥?strong>鈥嬫媶闆朵欢鈥?/strong>鈥嬶細0.58 + 0.00333...
2. 鈥?strong>鈥嬪悇鑷嚮鐮粹€?/strong>鈥嬶細
   • 0.58鐩存帴鍐?8/100
   • 0.00333...鐢ㄨ€佸姙娉曪細璁緔=0.00333...
     涔?0寰?0y=0.0333...
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3. 鈥?strong>鈥嬫嫾绉湪鈥?/strong>鈥嬶細58/100 +1/300 = 174/300 +1/300 = 175/300 = 7/12

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鍥涖€佸繀鍧戞寚鍗椻€斺€旀柊鎵嬪父鐘殑3涓敊璇?/h3>

1. 鈥?strong>鈥嬪惊鐜妭鎵鹃敊鈥?/strong>鈥嬶細姣斿鎶?.1234234234...鐨勫惊鐜妭褰撴垚"34"锛屽叾瀹炲簲璇ユ槸"234"
2. 鈥?strong>鈥嬪繕绾﹀垎鈥?/strong>鈥嬶細63/99涓嶅寲绠€鍒?/11锛岃€冭瘯瑕佹墸姝ラ鍒嗭紒
3. 鈥?strong>鈥嬬鍙蜂贡鏍団€?/strong>鈥嬶細鍐?.3虈鏃跺埆鎶婄偣鎵撳湪鏁板瓧涓棿锛屽緱鏍囧湪寰幆鑺傞灏句笂鏂?/li>

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浜斻€佹楠屾垚鏋滃皬濡欐嫑

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锛堟尃澶达級璇濊鎴戠涓€娆＄敤杩欐柟娉曟椂锛屾娲讳笉淇?.999...绛変簬1銆傚悗鏉ョ敤鍏紡涓€濂楋細璁緓=0.999...锛?0x=9.999...锛屼袱寮忕浉鍑忓緱9x=9 鈫?x=1銆傚ソ瀹朵紮锛屾暟瀛︽湁鏃跺€欑湡鍍忓彉榄旀湳锛?/p>

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