{"segment":[{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai8/lv3/img\/7.jpg' \/><\/center> Gi\u00e1 tr\u1ecb c\u1ee7a $ M = \\dfrac{0,1(6) + 0,(3)}{0,(3) + 1,1(6)}$ l\u00e0: ","select":["A. $3$ ","B. $0,(3)$ ","C. $\\dfrac{23}{73}$ ","D. $\\dfrac{19}{119}$"],"explain":" Ta c\u00f3: $M = \\dfrac{0,1(6) + 0,(3)}{0,(3) + 1,1(6)} \\\\ = \\dfrac{\\dfrac{16-1}{90}+\\dfrac{3}{9}}{\\dfrac{3}{9}+1+\\dfrac{16-1}{90}} \\\\ = \\dfrac{\\dfrac{1}{2}}{\\dfrac{3}{2}} \\\\ = \\dfrac{1}{3} = 0,(3)$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":4}]}],"id_ques":391},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" T\u00ecm $x$ bi\u1ebft: <br\/> $0,(17) : 2,(3) = x : 0,(3) $ ","select":["A. $ x = \\dfrac{17}{69} $ ","B. $ x = 9\\dfrac{51}{2300} $ ","C. $x = \\dfrac{17}{693} $","D. $x = \\dfrac{17}{231} $ "],"explain":"Ta c\u00f3: $0,(17) = \\dfrac{17}{99} \\\\ 0,(3) = \\dfrac{3}{9} = \\dfrac{1}{3} \\\\ 2,(3) = 2 + \\dfrac{3}{9} = \\dfrac{7}{3} $ <br\/> $\\Rightarrow 0,(17) : 2,(3) = x : 0,(3) $ <br\/> $ \\Rightarrow x : \\dfrac{1}{3} = \\dfrac{17}{99} : \\dfrac{7}{3} $ <br\/> $\\Rightarrow \\dfrac{1}{3}x = \\dfrac{17}{231} $ <br\/> $ \\Rightarrow x = \\dfrac{17}{231} . \\dfrac{1}{3} \\\\ \\Rightarrow x = \\dfrac{17}{693} $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":392},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[4]],"list":[{"point":10,"ques":" T\u00ecm $x $ bi\u1ebft: <br\/> $\\dfrac{0,1(6)+0,(3)}{0,(3)+1,1(6)} . x = 0,(2) $ ","select":["A. $ x = \\dfrac{73}{115}$ ","B. $x = \\dfrac{2}{9}$ ","C. $x = \\dfrac{1}{3}$ ","D. $ x = 0,(6) $ "],"explain":" Ta c\u00f3: $0,1(6) = \\dfrac{16-1}{90} = \\dfrac{1}{6} \\\\ 0,(3) = \\dfrac{3}{9} = \\dfrac{1}{3} \\\\ 1,1(6) = 1 + \\dfrac{16-1}{90} = \\dfrac{7}{6} \\\\ 0,(2) = \\dfrac{2}{9} $ <br\/> $ \\Rightarrow \\dfrac{0,1(6)+0,(3)}{0,(3)+1,1(6)} . x = 0,(2) $ <br\/> $\\Leftrightarrow \\dfrac{\\dfrac{1}{6}+\\dfrac{1}{3}}{\\dfrac{1}{3}+\\dfrac{7}{6}} . x = \\dfrac{2}{9} \\\\ \\Leftrightarrow \\dfrac{\\dfrac{1}{2}}{\\dfrac{3}{2}} . x = \\dfrac{2}{9} \\\\ \\Leftrightarrow \\dfrac{1}{3}.x = \\dfrac{2}{9} \\\\ \\Leftrightarrow x = \\dfrac{2}{3} = 0,(6) $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 D. <\/span><\/span> ","column":2}]}],"id_ques":393},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00fang hay sai","title_trans":"","temp":"true_false","correct":[["t","t","t","f"]],"list":[{"point":10,"image":"","col_name":["","\u0110\u00fang","Sai"],"arr_ques":[" $0,(1) = \\dfrac{1}{9} $ "," $ 0,(01) = \\dfrac{1}{99} $ "," $ 2,(459) = 2\\dfrac{17}{37} $ ","$ 1,(14) = \\dfrac{14}{99} $"],"hint":" \u00c1p d\u1ee5ng c\u00f4ng th\u1ee9c: <br\/> $ \\overline{t,(a_{1}a_{2}...a_{n})} = t + \\dfrac{\\overline{a_{1}a_{2}...a_{n}}}{\\underbrace{999...9}_{n}} $","explain":[" (\u0110\u00fang)","<br\/> (\u0110\u00fang) ","<br\/> (\u0110\u00fang). V\u00ec $2,(459) = 2 + \\dfrac{459}{999} = 2 + \\dfrac{17}{37} = 2\\dfrac{17}{37} $","<br\/> (Sai). V\u00ec $1,(14) = 1 + \\dfrac{14}{99} = \\dfrac{113}{99}$ "]}]}],"id_ques":394},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai8/lv3/img\/7.jpg' \/><\/center> T\u00ednh gi\u00e1 tr\u1ecb c\u1ee7a bi\u1ec3u th\u1ee9c $M = \\dfrac{0,(5) + 0,(3)-0,1(6)}{2,5+1,(6)-0,8(3)}$ ","select":["A. $\\dfrac{64}{327}$ ","B. $4,(615384)$ ","C. $0,21(6)$","D. $0,(216)$ "],"explain":" Ta c\u00f3: $M = \\dfrac{0,(5) + 0,(3)-0,(16)}{2,5+1,(6)-0,8(3)} \\\\ = \\dfrac{\\dfrac{5}{9}+\\dfrac{3}{9}-\\dfrac{16-1}{90}}{\\dfrac{5}{2}+1+\\dfrac{6}{9}-\\dfrac{83-8}{90}} \\\\ = \\dfrac{\\dfrac{13}{18}}{\\dfrac{10}{3}} \\\\ = \\dfrac{13}{60} = 0,21(6)$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":4}]}],"id_ques":395},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":"Cho $A = \\dfrac{7}{8.\\square}$ <br\/> C\u00f3 th\u1ec3 \u0111i\u1ec1n \u0111\u01b0\u1ee3c bao nhi\u00eau s\u1ed1 nguy\u00ean t\u1ed1 c\u00f3 m\u1ed9t ch\u1eef s\u1ed1 v\u00e0o $\\square$ \u0111\u1ec3 A l\u00e0 s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n? ","select":["A. 1 ","B. 2","C. 3","D. 5"],"hint":"\u0110\u1ec3 A l\u00e0 s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n th\u00ec ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n c\u1ee7a A c\u00f3 m\u1eabu kh\u00f4ng ch\u1ee9a c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 kh\u00e1c 2 v\u00e0 5. ","explain":" Ta c\u00f3: $A = \\dfrac{7}{8.\\square}$ <br\/> \u0110\u1ec3 A l\u00e0 s\u1ed1 th\u1eadp ph\u00e2n h\u1eefu h\u1ea1n th\u00ec ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n c\u1ee7a A c\u00f3 m\u1eabu kh\u00f4ng ch\u1ee9a c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 kh\u00e1c 2 v\u00e0 5. <br\/> Ta c\u00f3: 7 l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1, $\\square$ l\u00e0 s\u1ed1 nguy\u00ean t\u1ed1 c\u00f3 m\u1ed9t ch\u1eef s\u1ed1 (2, 3, 5, 7). <br\/> V\u00ec v\u1eady \u0111i\u1ec1n v\u00e0o \u00f4 vu\u00f4ng l\u00e0: 2,5 ho\u1eb7c 7 <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":4}]}],"id_ques":396},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":10,"ques":" <span class='basic_left'> Khi vi\u1ebft ph\u00e2n s\u1ed1 $\\dfrac{5}{7}$ d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n, h\u1ecfi ch\u1eef s\u1ed1 th\u1ee9 2017 sau d\u1ea5u ph\u1ea9y l\u00e0 ch\u1eef s\u1ed1 n\u00e0o? <\/span> ","select":["A. 7 ","B. 1","C. 4","D. 2"],"explain":" Nh\u1eadn x\u00e9t: Ph\u00e2n s\u1ed1 $\\dfrac{5}{7}$ l\u00e0 ph\u00e2n s\u1ed1 t\u1ed1i gi\u1ea3n c\u00f3 m\u1eabu l\u00e0 7 (c\u00f3 th\u1eeba s\u1ed1 nguy\u00ean t\u1ed1 kh\u00e1c 2 v\u00e0 5) n\u00ean vi\u1ebft \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n. <br\/> Ta c\u00f3 $\\dfrac{5}{7} = 0,(714285) = 0,714285 714285 714285....$ <br\/> S\u1ed1 th\u1eadp ph\u00e2n 0,(714285) l\u00e0 s\u1ed1 th\u1eadp ph\u00e2n v\u00f4 h\u1ea1n tu\u1ea7n ho\u00e0n c\u00f3 chu k\u00ec g\u1ed3m 6 ch\u1eef s\u1ed1. <br\/> Ta l\u1ea1i c\u00f3 2017 chia cho 6 d\u01b0 1 (v\u00ec 2017 = 6.336 + 1), <br\/> n\u00ean ch\u1eef s\u1ed1 th\u1eadp ph\u00e2n th\u1ee9 2017 sau d\u1ea5u ph\u1ea9y c\u1ee7a s\u1ed1 0,(714285) l\u00e0 7. <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":4}]}],"id_ques":397},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" So s\u00e1nh hai l\u0169y th\u1eeba sau: <br\/> $\\left(\\dfrac{9}{11} - 0,81\\right)^{2017}$ v\u00e0 $\\dfrac{1}{10^{4034}}$ ","select":["A. > ","B. = ","C. < "],"hint":" T\u00ednh gi\u00e1 tr\u1ecb bi\u1ec3u th\u1ee9c trong ngo\u1eb7c c\u1ee7a v\u1ebf tr\u00e1i sau \u0111\u00f3 vi\u1ebft th\u00e0nh t\u00edch c\u1ee7a hai l\u0169y th\u1eeba d\u1ef1a theo v\u1ebf ph\u1ea3i$","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> L\u01b0u \u00fd c\u00f4ng th\u1ee9c $(a.b)^{n} = a^{n} . b^{n}$ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $\\left(\\dfrac{9}{11} - 0,81\\right)^{2017} = \\left(\\dfrac{9}{11} - \\dfrac{81}{100} \\right)^{2017} \\\\ = \\left(\\dfrac{900-891}{1100}\\right)^{2017} = \\left(\\dfrac{9}{1100}\\right)^{2017} \\\\ = \\left(\\dfrac{9}{11} . \\dfrac{1}{100} \\right)^{2017} = \\left(\\dfrac{9}{11}\\right)^{2017} . \\left(\\dfrac{1}{100}\\right)^{2017} \\\\ = \\left(\\dfrac{9}{11}\\right)^{2017} . \\dfrac{1}{10^{2.2017}} \\\\ = \\left(\\dfrac{9}{11}\\right)^{2017} . \\dfrac{1}{10^{4034}} < \\dfrac{1}{10^{4034}} \\,(do\\,\\dfrac{9}{11} <1)$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> <span class='basic_left'> <u> Nh\u1eadn x\u00e9t<\/u> : <br\/> T\u1eeb \u0111\u00e2y ta c\u0169ng suy ra $\\left(\\dfrac{9}{11} - 0,81\\right)^{2017}$ c\u00f3 \u00edt nh\u1ea5t 4033 ch\u1eef s\u1ed1 0 \u0111\u1ea7u ti\u00ean ngay sau d\u1ea5u ph\u1ea9y th\u1eadp ph\u00e2n. <\/span> ","column":3}]}],"id_ques":398},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":10,"ques":" T\u00ecm $x$ bi\u1ebft: <br\/> $0,(12) : (x-1) = 1,(6) : 0,(4)$ ","select":["A. $ x = 1,(32)$ ","B. $x = 1,(032)$ ","C. $x = 1,0(32)$ ","D. $ x = 1,03(2)$ "],"explain":" Ta c\u00f3: $0,(12) = \\dfrac{12}{99} = \\dfrac{4}{33} \\\\ 0,(4) = \\dfrac{4}{9} \\\\ 1,(6) = 1 + \\dfrac{6}{9} = \\dfrac{5}{3} $ <br\/> $\\Rightarrow 0,(12) : (x-1) = 1,(6) : 0,(4) \\\\ \\Rightarrow \\dfrac{4}{33} : (x-1) = \\dfrac{5}{3} : \\dfrac{4}{9} \\\\ \\Rightarrow \\dfrac{4}{33} : (x-1) = \\dfrac{15}{4} $ <br\/> $ \\Rightarrow x - 1 =\\dfrac{4}{33} : \\dfrac{15}{4}$ <br\/> $\\Rightarrow x = \\dfrac{16}{495} \\\\ \\Rightarrow x = \\dfrac{16}{495} + 1 \\\\ \\Rightarrow x= \\dfrac{511}{495} = 1,0(32) $ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":399},{"time":24,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":10,"ques":" T\u00ecm $x$ bi\u1ebft: <br\/> $x . 0,(2) + 1,2(25) = 2,3(15) $ ","select":["A. $x = 4,9$ ","B. $x = 4,90(45)$ ","C. $x = 4,9(45)$ ","D. $x = 4,91$ "],"explain":"Ta c\u00f3: $2,3(15) = 2 + \\dfrac{315-3}{990} = 2 + \\dfrac{312}{990} = \\dfrac{2292}{990}\\\\ 1,2(25) = 1 + \\dfrac{225-2}{990} = 1 + \\dfrac{223}{990} = \\dfrac{1213}{990} \\\\ 0,(2) = \\dfrac{2}{9}$ <br\/> $\\Rightarrow x . 0,(2) + 1,2(25) = 2,3(15) \\\\ \\Rightarrow x . \\dfrac{2}{9} = \\dfrac{2292}{990} - \\dfrac{1213}{990} $ <br\/> $ \\Rightarrow x.\\dfrac{2}{9} = \\dfrac{1079}{990} $ <br\/> $ \\Rightarrow x = \\dfrac{1079}{990}: \\dfrac{2}{9}$ <br\/> $\\Rightarrow = \\dfrac{1079}{220} = 4,90(45)$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":400}],"lesson":{"save":0,"level":3}}