# Repeating Decimal as a Fraction

## How to write repeating Decimal as a Fraction?

To convert a repeating decimal to a fraction, you set up an equation where the repeating decimal equals a variable, multiply to shift the repeating part, subtract to eliminate the repeating part, and solve for the variable. This method works for any repeating decimal.

To conversion repeating Decimal number to Fraction use this fromula, which is given below-

(D x 10R) - N/10R -1

Where,

• D = The whole decimal number;
• R = Count the number of repeating part of decimal number;
• N = Value of non-repeating part of decimal number;
Decimal Repeating as a Fraction
Simplified Mixed
0.2 2/9
0.6 2/3
0.3 1/3
1.3 4/3 1 1/3
0.1 1/9
0.8 8/9
1.6 5/3 1 2/3
0.7 7/9
1.21 40/33 1 7/33
.16 16/99
0.83 83/99
0.4 4/9
.27 3/11
0.83333 83333/99999
2.6 8/3 2 2/3
2.3 7/3 2 1/3
0.5 5/9
1.83 182/99 1 83/99
2.16 214/99 2 16/99
.45 5/11
0.23 23/99
.9 1/1 1 0/1
3.83 380/99 3 83/99
.083 83/999
.18 2/11
.44444 4/9
3.2 29/9 3 2/9
.81 9/11
3.1 28/9 3 1/9
0.11111 1/9
1.5 14/9 1 5/9
.72 8/11
0.18 2/11
.09 1/11
3.5 32/9 3 5/9
3.3 10/3 3 1/3
.36 4/11
2.8 26/9 2 8/9
1.27 14/11 1 3/11
0.36 4/11
.13 13/99
3.16 313/99 3 16/99
1.77777 16/9 1 7/9
1.66666 5/3 1 2/3
.11111 1/9
5.3 16/3 5 1/3
0.194 194/999
0.54 6/11
0.45 5/11
.23 23/99
0.12 4/33
0.15 5/33
1.1 10/9 1 1/9
.123 41/333
0.135 5/37
1.16 38/33 1 5/33
.26 26/99
8.3 25/3 8 1/3
.12 4/33
0.09 1/11
3.25 322/99 3 25/99
.3636 4/11
.1666 1666/9999
.8333 8333/9999
2.2 20/9 2 2/9
4.3 13/3 4 1/3
.46 46/99
2.14 212/99 2 14/99
.87 29/33
.67 67/99
0.26 26/99
0.06 2/33
0.05 5/99
.3333 1/3
.02 2/99
0.185 5/27
3.48 115/33 3 16/33
0.64 64/99
.24 8/33
.05 5/99
.16666 16666/99999
0.51 17/33
0.78 26/33
.135 5/37
6.6 20/3 6 2/3
4.6 14/3 4 2/3
.888 8/9
3.33333 10/3 3 1/3
0.03 1/33
0.82 82/99
0.123 41/333
.63 7/11
1.63 18/11 1 7/11
0.80 8/9
0.44 4/9
.222 2/9
.185 5/27
0.1666 1666/9999
.39 13/33
.37 37/99
0.46 46/99
0.66666 2/3
.14 14/99
9.09 100/11 9 1/11
0.21 7/33
0.416 416/999
2.314 2312/999 2 314/999
.666 2/3
.38 38/99
2.7 25/9 2 7/9
2.33333 7/3 2 1/3
5.6 17/3 5 2/3
.833 833/999
0.73 73/99
4.4 40/9 4 4/9
.66 2/3
.583 583/999
1.32 131/99 1 32/99
.03 1/33
.333 1/3
.75 25/33
0.44444 4/9
.56 56/99
2.267 755/333 2 89/333
.25 25/99
2.83 281/99 2 83/99
.77 7/9
.166 166/999
0.02 2/99
1.2 11/9 1 2/9
0.16666 16666/99999
0.13 13/99
3.53 350/99 3 53/99
2.31 229/99 2 31/99
10.6 32/3 10 2/3
.22 2/9
0.79 79/99
.58 19/33
.037 1/27
0.55 5/9
.296 8/27
.22222 2/9
.08333 8333/99999
2.5 23/9 2 5/9
.96 32/33
0.32 32/99
4.45 49/11 4 5/11
.08 8/99
0.86 86/99
1.54 17/11 1 6/11
0.66 2/3
.33 1/3
0.63 7/11
0.116 116/999
.21 7/33
.55 5/9
0.48 16/33
1.4 13/9 1 4/9
.33333 1/3
0.14 14/99
.44 4/9
0.55555 5/9
1.83333 183332/99999 1 83333/99999
3.27 36/11 3 3/11
1.24 41/33 1 8/33
0.111 1/9
3.7 34/9 3 7/9
1.81 20/11 1 9/11
0.38 38/99
.51 17/33
3.24 107/33 3 8/33
.88 8/9
7.3 22/3 7 1/3
0.22 2/9
4.135 153/37 4 5/37
0.57 57/99
13.3 40/3 13 1/3
2.67 265/99 2 67/99
3.63 40/11 3 7/11
0.126 14/111
0.91 91/99

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