To turn a repeating decimal into a fraction, call it x, multiply by a power of 10 so the repeating blocks line up, subtract, and solve. For example 0.333… = 3/9 = 1/3. Pick a decimal below for the full worked answer, or use the decimal to fraction converter. For decimals that stop, see the terminating decimal chart.
0.111… = 1/9 · 0.222… = 2/9 · 0.333… = 1/3 · 0.444… = 4/9 · 0.555… = 5/9 · 0.666… = 2/3 · 0.777… = 7/9 · 0.888… = 8/9 · 1.111… = 10/9 · 1.222… = 11/9 · 1.333… = 4/3 · 1.444… = 13/9 · 1.555… = 14/9 · 1.666… = 5/3 · 1.777… = 16/9 · 1.888… = 17/9 · 2.111… = 19/9 · 2.222… = 20/9 · 2.333… = 7/3 · 2.444… = 22/9 · 2.555… = 23/9 · 2.666… = 8/3 · 2.777… = 25/9 · 2.888… = 26/9 · 3.111… = 28/9 · 3.222… = 29/9 · 3.333… = 10/3 · 3.444… = 31/9 · 3.555… = 32/9 · 3.666… = 11/3 · 3.777… = 34/9 · 3.888… = 35/9 · 4.111… = 37/9 · 4.222… = 38/9 · 4.333… = 13/3 · 4.444… = 40/9 · 4.555… = 41/9 · 4.666… = 14/3 · 4.777… = 43/9 · 4.888… = 44/9 · 5.111… = 46/9 · 5.222… = 47/9 · 5.333… = 16/3 · 5.444… = 49/9 · 5.555… = 50/9 · 5.666… = 17/3 · 5.777… = 52/9 · 5.888… = 53/9 · 6.111… = 55/9 · 6.222… = 56/9 · 6.333… = 19/3 · 6.444… = 58/9 · 6.555… = 59/9 · 6.666… = 20/3 · 6.777… = 61/9 · 6.888… = 62/9 · 7.111… = 64/9 · 7.222… = 65/9 · 7.333… = 22/3 · 7.444… = 67/9 · 7.555… = 68/9 · 7.666… = 23/3 · 7.777… = 70/9 · 7.888… = 71/9 · 8.111… = 73/9 · 8.222… = 74/9 · 8.333… = 25/3 · 8.444… = 76/9 · 8.555… = 77/9 · 8.666… = 26/3 · 8.777… = 79/9 · 8.888… = 80/9 · 9.111… = 82/9 · 9.222… = 83/9 · 9.333… = 28/3 · 9.444… = 85/9 · 9.555… = 86/9 · 9.666… = 29/3 · 9.777… = 88/9 · 9.888… = 89/9
0.010101… = 1/99 · 0.020202… = 2/99 · 0.030303… = 1/33 · 0.040404… = 4/99 · 0.050505… = 5/99 · 0.060606… = 2/33 · 0.070707… = 7/99 · 0.080808… = 8/99 · 0.090909… = 1/11 · 0.101010… = 10/99 · 0.121212… = 4/33 · 0.131313… = 13/99 · 0.141414… = 14/99 · 0.151515… = 5/33 · 0.161616… = 16/99 · 0.171717… = 17/99 · 0.181818… = 2/11 · 0.191919… = 19/99 · 0.202020… = 20/99 · 0.212121… = 7/33 · 0.232323… = 23/99 · 0.242424… = 8/33 · 0.252525… = 25/99 · 0.262626… = 26/99 · 0.272727… = 3/11 · 0.282828… = 28/99 · 0.292929… = 29/99 · 0.303030… = 10/33 · 0.313131… = 31/99 · 0.323232… = 32/99 · 0.343434… = 34/99 · 0.353535… = 35/99 · 0.363636… = 4/11 · 0.373737… = 37/99 · 0.383838… = 38/99 · 0.393939… = 13/33 · 0.404040… = 40/99 · 0.414141… = 41/99 · 0.424242… = 14/33 · 0.434343… = 43/99 · 0.454545… = 5/11 · 0.464646… = 46/99 · 0.474747… = 47/99 · 0.484848… = 16/33 · 0.494949… = 49/99 · 0.505050… = 50/99 · 0.515151… = 17/33 · 0.525252… = 52/99 · 0.535353… = 53/99 · 0.545454… = 6/11 · 0.565656… = 56/99 · 0.575757… = 19/33 · 0.585858… = 58/99 · 0.595959… = 59/99 · 0.606060… = 20/33 · 0.616161… = 61/99 · 0.626262… = 62/99 · 0.636363… = 7/11 · 0.646464… = 64/99 · 0.656565… = 65/99 · 0.676767… = 67/99 · 0.686868… = 68/99 · 0.696969… = 23/33 · 0.707070… = 70/99 · 0.717171… = 71/99 · 0.727272… = 8/11 · 0.737373… = 73/99 · 0.747474… = 74/99 · 0.757575… = 25/33 · 0.767676… = 76/99 · 0.787878… = 26/33 · 0.797979… = 79/99 · 0.808080… = 80/99 · 0.818181… = 9/11 · 0.828282… = 82/99 · 0.838383… = 83/99 · 0.848484… = 28/33 · 0.858585… = 85/99 · 0.868686… = 86/99 · 0.878787… = 29/33 · 0.898989… = 89/99 · 0.909090… = 10/11 · 0.919191… = 91/99 · 0.929292… = 92/99 · 0.939393… = 31/33 · 0.949494… = 94/99 · 0.959595… = 95/99 · 0.969696… = 32/33 · 0.979797… = 97/99 · 0.989898… = 98/99
0.001001001… = 1/999 · 0.002002002… = 2/999 · 0.003003003… = 1/333 · 0.004004004… = 4/999 · 0.005005005… = 5/999 · 0.006006006… = 2/333 · 0.007007007… = 7/999 · 0.008008008… = 8/999 · 0.009009009… = 1/111 · 0.012012012… = 4/333 · 0.012345012345012345… = 4115/333333 · 0.027027027… = 1/37 · 0.037037037… = 1/27 · 0.054054054… = 2/37 · 0.074074074… = 2/27 · 0.076076076… = 76/999 · 0.076923076923076923… = 1/13 · 0.081081081… = 3/37 · 0.123123123… = 41/333 · 0.135135135… = 5/37 · 0.142142142… = 142/999 · 0.142857142857142857… = 1/7 · 0.153153153… = 17/111 · 0.185185185… = 5/27 · 0.230230230… = 230/999 · 0.234234234… = 26/111 · 0.285285285… = 95/333 · 0.307307307… = 307/999 · 0.345345345… = 115/333 · 0.384384384… = 128/333 · 0.428428428… = 428/999 · 0.456456456… = 152/333 · 0.461461461… = 461/999 · 0.538538538… = 538/999 · 0.567567567… = 21/37 · 0.571571571… = 571/999 · 0.615615615… = 205/333 · 0.678678678… = 226/333 · 0.692692692… = 692/999 · 0.714714714… = 238/333 · 0.769769769… = 769/999 · 0.789789789… = 263/333 · 0.846846846… = 94/111 · 0.857857857… = 857/999 · 0.923923923… = 923/999
0.0111… = 1/90 · 0.0222… = 1/45 · 0.0333… = 1/30 · 0.0444… = 2/45 · 0.0555… = 1/18 · 0.0666… = 1/15 · 0.0777… = 7/90 · 0.08333… = 1/12 · 0.08666… = 13/150 · 0.0888… = 4/45 · 0.1222… = 11/90 · 0.1333… = 2/15 · 0.1444… = 13/90 · 0.1555… = 7/45 · 0.16333… = 49/300 · 0.1666… = 1/6 · 0.16666… = 1/6 · 0.1777… = 8/45 · 0.1888… = 17/90 · 0.2111… = 19/90 · 0.2333… = 7/30 · 0.2444… = 11/45 · 0.2555… = 23/90 · 0.2666… = 4/15 · 0.2777… = 5/18 · 0.2888… = 13/45 · 0.3111… = 14/45 · 0.3222… = 29/90 · 0.3444… = 31/90 · 0.3555… = 16/45 · 0.3666… = 11/30 · 0.3777… = 17/45 · 0.3888… = 7/18 · 0.4111… = 37/90 · 0.41333… = 31/75 · 0.41666… = 5/12 · 0.4222… = 19/45 · 0.4333… = 13/30 · 0.4555… = 41/90 · 0.4666… = 7/15 · 0.4777… = 43/90 · 0.4888… = 22/45 · 0.5111… = 23/45 · 0.5222… = 47/90 · 0.5333… = 8/15 · 0.5444… = 49/90 · 0.5666… = 17/30 · 0.5777… = 26/45 · 0.58333… = 7/12 · 0.58666… = 44/75 · 0.5888… = 53/90 · 0.6111… = 11/18 · 0.6222… = 28/45 · 0.6333… = 19/30 · 0.6444… = 29/45 · 0.6555… = 59/90 · 0.6777… = 61/90 · 0.6888… = 31/45 · 0.7111… = 32/45 · 0.7222… = 13/18 · 0.7333… = 11/15 · 0.7444… = 67/90 · 0.75333… = 113/150 · 0.7555… = 34/45 · 0.75666… = 227/300 · 0.7666… = 23/30 · 0.7888… = 71/90 · 0.8111… = 73/90 · 0.8222… = 37/45 · 0.8333… = 5/6 · 0.83333… = 5/6 · 0.83666… = 251/300 · 0.8444… = 38/45 · 0.8555… = 77/90 · 0.8666… = 13/15 · 0.8777… = 79/90 · 0.9111… = 41/45 · 0.91333… = 137/150 · 0.91666… = 11/12 · 0.9222… = 83/90 · 0.9333… = 14/15 · 0.9444… = 17/18 · 0.9555… = 43/45 · 0.9666… = 29/30 · 0.9777… = 44/45 · 0.9888… = 89/90 · 1.1666… = 7/6 · 1.8333… = 11/6 · 2.1666… = 13/6 · 2.5333… = 38/15 · 3.8333… = 23/6