127 個分數與它們的小數
分母不超過 20 的全部最簡分數。小數是按直式一位一位除出來的，所以循環節是精確的——0.1(6)，不是 0.1666…
按分母
分母只由 2 和 5 組成時小數會除盡，摻進 3 或 7 就會循環。因為 10 = 2 × 5。
/2有限小數
1/20.550%
/3循環小數
1/30.(3)33.(3)%2/30.(6)66.(6)%
/4有限小數
1/40.2525%3/40.7575%
/5有限小數
1/50.220%2/50.440%3/50.660%4/50.880%
/6循環小數
1/60.1(6)16.(6)%5/60.8(3)83.(3)%
/7循環小數
1/70.(142857)14.(285714)%2/70.(285714)28.(571428)%3/70.(428571)42.(857142)%4/70.(571428)57.(142857)%5/70.(714285)71.(428571)%6/70.(857142)85.(714285)%
/8有限小數
1/80.12512.5%3/80.37537.5%5/80.62562.5%7/80.87587.5%
/9循環小數
1/90.(1)11.(1)%2/90.(2)22.(2)%4/90.(4)44.(4)%5/90.(5)55.(5)%7/90.(7)77.(7)%8/90.(8)88.(8)%
/10有限小數
1/100.110%3/100.330%7/100.770%9/100.990%
/11循環小數
1/110.(09)9.(09)%2/110.(18)18.(18)%3/110.(27)27.(27)%4/110.(36)36.(36)%5/110.(45)45.(45)%6/110.(54)54.(54)%7/110.(63)63.(63)%8/110.(72)72.(72)%9/110.(81)81.(81)%10/110.(90)90.(90)%
/12循環小數
1/120.08(3)8.(3)%5/120.41(6)41.(6)%7/120.58(3)58.(3)%11/120.91(6)91.(6)%
/13循環小數
1/130.(076923)7.(692307)%2/130.(153846)15.(384615)%3/130.(230769)23.(076923)%4/130.(307692)30.(769230)%5/130.(384615)38.(461538)%6/130.(461538)46.(153846)%7/130.(538461)53.(846153)%8/130.(615384)61.(538461)%9/130.(692307)69.(230769)%10/130.(769230)76.(923076)%11/130.(846153)84.(615384)%12/130.(923076)92.(307692)%
/14循環小數
1/140.0(714285)7.(142857)%3/140.2(142857)21.(428571)%5/140.3(571428)35.(714285)%9/140.6(428571)64.(285714)%11/140.7(857142)78.(571428)%13/140.9(285714)92.(857142)%
/15循環小數
1/150.0(6)6.(6)%2/150.1(3)13.(3)%4/150.2(6)26.(6)%7/150.4(6)46.(6)%8/150.5(3)53.(3)%11/150.7(3)73.(3)%13/150.8(6)86.(6)%14/150.9(3)93.(3)%
/16有限小數
1/160.06256.25%3/160.187518.75%5/160.312531.25%7/160.437543.75%9/160.562556.25%11/160.687568.75%13/160.812581.25%15/160.937593.75%
/17循環小數
1/170.(0588235294117647)5.(8823529411764705)%2/170.(1176470588235294)11.(7647058823529411)%3/170.(1764705882352941)17.(6470588235294117)%4/170.(2352941176470588)23.(5294117647058823)%5/170.(2941176470588235)29.(4117647058823529)%6/170.(3529411764705882)35.(2941176470588235)%7/170.(4117647058823529)41.(1764705882352941)%8/170.(4705882352941176)47.(0588235294117647)%9/170.(5294117647058823)52.(9411764705882352)%10/170.(5882352941176470)58.(8235294117647058)%11/170.(6470588235294117)64.(7058823529411764)%12/170.(7058823529411764)70.(5882352941176470)%13/170.(7647058823529411)76.(4705882352941176)%14/170.(8235294117647058)82.(3529411764705882)%15/170.(8823529411764705)88.(2352941176470588)%16/170.(9411764705882352)94.(1176470588235294)%
/18循環小數
1/180.0(5)5.(5)%5/180.2(7)27.(7)%7/180.3(8)38.(8)%11/180.6(1)61.(1)%13/180.7(2)72.(2)%17/180.9(4)94.(4)%
/19循環小數
1/190.(052631578947368421)5.(263157894736842105)%2/190.(105263157894736842)10.(526315789473684210)%3/190.(157894736842105263)15.(789473684210526315)%4/190.(210526315789473684)21.(052631578947368421)%5/190.(263157894736842105)26.(315789473684210526)%6/190.(315789473684210526)31.(578947368421052631)%7/190.(368421052631578947)36.(842105263157894736)%8/190.(421052631578947368)42.(105263157894736842)%9/190.(473684210526315789)47.(368421052631578947)%10/190.(526315789473684210)52.(631578947368421052)%11/190.(578947368421052631)57.(894736842105263157)%12/190.(631578947368421052)63.(157894736842105263)%13/190.(684210526315789473)68.(421052631578947368)%14/190.(736842105263157894)73.(684210526315789473)%15/190.(789473684210526315)78.(947368421052631578)%16/190.(842105263157894736)84.(210526315789473684)%17/190.(894736842105263157)89.(473684210526315789)%18/190.(947368421052631578)94.(736842105263157894)%
/20有限小數
1/200.055%3/200.1515%7/200.3535%9/200.4545%11/200.5555%13/200.6565%17/200.8585%19/200.9595%
/21循環小數
1/210.(047619)4.(761904)%2/210.(095238)9.(523809)%4/210.(190476)19.(047619)%5/210.(238095)23.(809523)%8/210.(380952)38.(095238)%10/210.(476190)47.(619047)%11/210.(523809)52.(380952)%13/210.(619047)61.(904761)%16/210.(761904)76.(190476)%17/210.(809523)80.(952380)%19/210.(904761)90.(476190)%20/210.(952380)95.(238095)%
/22循環小數
1/220.0(45)4.(54)%3/220.1(36)13.(63)%5/220.2(27)22.(72)%7/220.3(18)31.(81)%9/220.4(09)40.(90)%13/220.5(90)59.(09)%15/220.6(81)68.(18)%17/220.7(72)77.(27)%19/220.8(63)86.(36)%21/220.9(54)95.(45)%
/23循環小數
1/230.(0434782608695652173913)4.(3478260869565217391304)%2/230.(0869565217391304347826)8.(6956521739130434782608)%3/230.(1304347826086956521739)13.(0434782608695652173913)%4/230.(1739130434782608695652)17.(3913043478260869565217)%5/230.(2173913043478260869565)21.(7391304347826086956521)%6/230.(2608695652173913043478)26.(0869565217391304347826)%7/230.(3043478260869565217391)30.(4347826086956521739130)%8/230.(3478260869565217391304)34.(7826086956521739130434)%9/230.(3913043478260869565217)39.(1304347826086956521739)%10/230.(4347826086956521739130)43.(4782608695652173913043)%11/230.(4782608695652173913043)47.(8260869565217391304347)%12/230.(5217391304347826086956)52.(1739130434782608695652)%13/230.(5652173913043478260869)56.(5217391304347826086956)%14/230.(6086956521739130434782)60.(8695652173913043478260)%15/230.(6521739130434782608695)65.(2173913043478260869565)%16/230.(6956521739130434782608)69.(5652173913043478260869)%17/230.(7391304347826086956521)73.(9130434782608695652173)%18/230.(7826086956521739130434)78.(2608695652173913043478)%19/230.(8260869565217391304347)82.(6086956521739130434782)%20/230.(8695652173913043478260)86.(9565217391304347826086)%21/230.(9130434782608695652173)91.(3043478260869565217391)%22/230.(9565217391304347826086)95.(6521739130434782608695)%
/24循環小數
1/240.041(6)4.1(6)%5/240.208(3)20.8(3)%7/240.291(6)29.1(6)%11/240.458(3)45.8(3)%13/240.541(6)54.1(6)%17/240.708(3)70.8(3)%19/240.791(6)79.1(6)%23/240.958(3)95.8(3)%
怎麼看這一頁
- 括號裡的數字無限重複——0.1(6) 就是 0.16666…
- 分母除了 2 和 5 沒有別的質因數時，小數就會除盡。
- 等值分數不另設地址：查 2/4 會到 1/2。
- 百分比是同一個數乘 100，度數是同一個數乘 360，只是乘數不同。
常見問題
Q0.375 是幾分之幾？
八分之三。能除盡的小數來自只由 2 和 5 組成的分母，所以像 0.375 這樣三位就結束的小數，分母是 8。
Q為什麼沒有 2/4？
因為它和 1/2 是同一個數。同一個值給兩個地址，一個答案就被兩頁分走了。
Q0.(3) 這種寫法是什麼意思？
括號裡的部分無限重複。0.(3) 就是 0.3333…，0.1(6) 就是 0.16666…
Q哪些分數會變成循環小數？
分母裡有 2 和 5 以外的質因數的那些——因為 10 = 2 × 5。
Q為什麼只到分母 20？
因為人們拿著小數來找的分數基本都在這裡面：2 的冪（2、4、8、16）、5、10、20，還有常用的 3、6、7、9、12。