Decimal as a Fraction

Converting a decimal number to a fraction involves expressing the decimal as a ratio of two integers. This process is straightforward for terminating decimals but requires special techniques for repeating decimals.

0.375 Decimal = 3/8 as a Fraction

Step-by-Step Calculation:

How to Convert Decimal to Fraction

To convert a decimal number to a fraction, follow these steps:

  • Regular Decimals: Count decimal places, write as fraction with denominator as power of 10, then simplify.
  • Repeating Decimals: Use algebraic method - multiply by powers of 10 to align repeating parts, then subtract to eliminate repetition.
  • Simplification: Find the Greatest Common Divisor (GCD) and divide both numerator and denominator by it.

Decimal to Fraction Conversion Examples

Here are some examples of decimal numbers converted to fractions:

Decimal Fraction
Simplified Mixed
.375 3/8
.625 5/8
.875 7/8
1.125 9/8 11/8
0.125 1/8
1.5 3/2 11/2
0.375 3/8
2.5 5/2 21/2
1.25 5/4 11/4
.1875 3/16
0.5 1/2
0.0625 1/16
0.6 3/5
0.2 1/5
0.25 1/4
.3125 5/16
.6875 11/16
.75 3/4
.4375 7/16
2.25 9/4 21/4
0.3 3/10
0.4 2/5
0.8 4/5
3.5 7/2 31/2
.8125 13/16
1.6 8/5 13/5
4.5 9/2 41/2
.9375 15/16
.5625 9/16
0.1 1/10
.16 4/25
.15 3/20
1.3 13/10 13/10
.08 2/25
1.875 15/8 17/8
1.75 7/4 13/4
1.4 7/5 12/5
6.25 25/4 61/4
.83 83/100
0.05 1/20
1.8 9/5 14/5
1.375 11/8 13/8
.325 13/40
3.75 15/4 33/4
2.4 12/5 22/5
0.16 4/25
.7 7/10
.66 33/50
0.04 1/25
0.9 9/10
2.6 13/5 23/5
0.08 2/25
.35 7/20
.04 1/25
.65 13/20
0.7 7/10
0.45 9/20
0.35 7/20
.85 17/20
0.15 3/20
2.3 23/10 23/10
.33 33/100
7.5 15/2 71/2
.13 13/100
12.5 25/2 121/2
.45 9/20
2.75 11/4 23/4
4.8 24/5 44/5
3.6 18/5 33/5
.675 27/40
.175 7/40
.12 3/25
.88 22/25
.14 7/50
1.625 13/8 15/8
.67 67/100
.025 1/40
5.5 11/2 51/2
.825 33/40
.02 1/50
.36 9/25
3.25 13/4 31/4
0.06 3/50
0.65 13/20
.083 83/1000
0.3125 5/16
2.8 14/5 24/5
.64 16/25
0.33 33/100
.63 63/100
.187 187/1000
.03125 1/32
.167 167/1000
.62 31/50
.188 47/250
.11 11/100
.84 21/25
.28 7/25
0.5625 9/16
1.7 17/10 17/10
1.33 133/100 133/100
.9 9/10
.78 39/50
.32 8/25
.075 3/40
6.5 13/2 61/2
.19 19/100
.18 9/50
0.03125 1/32
4.25 17/4 41/4
.68 17/25
2.9 29/10 29/10
0.12 3/25
5.25 21/4 51/4
.8333 8333/10000
0.24 6/25
.09375 3/32
.15625 5/32
.31 31/100
.333 333/1000
2.33333 233333/100000 233333/100000
.667 667/1000
2.2 11/5 21/5
.38 19/50
.58 29/50
.666 333/500
0.4375 7/16
.42 21/50
3.375 27/8 33/8
3.2 16/5 31/5
.69 69/100
0.32 8/25
.55 11/20
0.64 16/25
.43 43/100
.72 18/25
2.375 19/8 23/8
.07 7/100
.86 43/50
.83333 83333/100000
0.83 83/100
.118 59/500
.37 37/100
.03 3/100
0.85 17/20
10.5 21/2 101/2
.225 9/40
.34375 11/32
2.625 21/8 25/8
.185 37/200
5.6 28/5 53/5
.09 9/100
1.33333 133333/100000 133333/100000
6.75 27/4 63/4
.34 17/50
3.8 19/5 34/5
.275 11/40
.312 39/125
0.38 19/50
.20 1/5
0.55 11/20
0.07 7/100
.156 39/250
.166 83/500
3.4 17/5 32/5
.01 1/100
0.44 11/25
0.008 1/125
.41 41/100
.44 11/25
0.015625 1/64
.94 47/50
.78125 25/32
.11111 11111/100000
.71 71/100
.29 29/100
.40625 13/32
1.333 1333/1000 1333/1000
.59 59/100
.87 87/100
0.333 333/1000
.89 89/100
3.125 25/8 31/8
0.09 9/100
.27 27/100
0.01 1/100
3.3 33/10 33/10
1.15 23/20 13/20
0.66 33/50
0.14 7/50
37.5 75/2 371/2
.22 11/50
0.28 7/25
0.48 12/25
.093 93/1000
0.03 3/100
.61 61/100
0.36 9/25
0.95 19/20
2.125 17/8 21/8
.120 3/25
4.2 21/5 41/5
.71875 23/32
.1666 833/5000
.833 833/1000
3.33 333/100 333/100
1.66 83/50 133/50
4.75 19/4 43/4
0.8125 13/16
8.75 35/4 83/4
.065 13/200
0.075 3/40
.46875 15/32
.84375 27/32
4.6 23/5 43/5
.95 19/20
0.63 63/100
9.14 457/50 97/50
9.35 187/20 97/20
0.81818 40909/50000
.866 433/500
0.004 1/250
0.26 13/50
0.42 21/50
7.2 36/5 71/5
0.17 17/100
2.1 21/10 21/10
5.75 23/4 53/4
0.08333 8333/100000
0.72 18/25
2.875 23/8 27/8
9.6 48/5 93/5
1.9 19/10 19/10
0.66666667 66666667/100000000
.17 17/100
4.125 33/8 41/8
0.58 29/50
0.83333 83333/100000
1.5625 25/16 19/16
0.56 14/25
3.625 29/8 35/8
0.001 1/1000
0.083 83/1000
.24 6/25
5.625 45/8 55/8
0.005 1/200
0.11111 11111/100000
0.33333 33333/100000
.060 3/50
8.4 42/5 82/5
0.39 39/100
0.11111111111 2147483647/2147483647
87.5 175/2 871/2
.66666 33333/50000
.59375 19/32
1.66666666667 4294967294/2147483647 12147483647/2147483647
1.16 29/25 14/25
0.225 9/40
0.57 57/100
.56 14/25
0.9375 15/16
1.05 21/20 11/20
0.167 167/1000
0.675 27/40
0.46 23/50
.425 17/40
5.3 53/10 53/10
.81 81/100
6.6 33/5 63/5
0.1019 1019/10000
0.53 53/100
0.667 667/1000
.008 1/125
4.4 22/5 42/5
2.025 81/40 21/40
20.25 81/4 201/4
.165 33/200
.30 3/10
.40 2/5
.50 1/2
.60 3/5
.70 7/10
.80 4/5
.90 9/10
0.82 41/50
0.08333333333 2147483647/2147483647
.96875 31/32
5.8 29/5 54/5
.035 7/200
.66667 66667/100000
.16667 16667/100000
0.43 43/100
1.45 29/20 19/20
.050 1/20
0.62 31/50
.583 583/1000
0.666 333/500
.21875 7/32
2.33 233/100 233/100
0.87 87/100
.078 39/500
0.84 21/25
0.425 17/40
.197 197/1000
.157 157/1000
22.5 45/2 221/2
3.14 157/50 37/50
5.2 26/5 51/5
2.66 133/50 233/50
1.6875 27/16 111/16
0.175 7/40
.015 3/200
1.83 183/100 183/100
2.3333 23333/10000 23333/10000
0.8333 8333/10000
0.31 31/100
.57 57/100
.53 53/100
.190 19/100
.22222 11111/50000
.08333 8333/100000
.005 1/200
.438 219/500
.39 39/100
9.5 19/2 91/2
0.16666666666 2147483647/2147483647
0.003 3/1000
.23 23/100
.77 77/100
.82 41/50
1.67 167/100 167/100
.812 203/250
.65625 21/32
.100 1/10
0.2826 1413/5000
.687 687/1000
1.08 27/25 12/25
.281 281/1000
.0375 3/80
6.2 31/5 61/5
7.4 37/5 72/5
7.875 63/8 77/8
1.65 33/20 113/20
.2666 1333/5000
.575 23/40
.018 9/500
62.5 125/2 621/2
4.625 37/8 45/8
.0875 7/80
.656 82/125

Conclusion

Converting decimals to fractions is a useful skill in mathematics. Whether dealing with regular or repeating decimals, the methods outlined above provide a clear path to expressing decimals as fractions. Practice with various decimal numbers to become proficient in these conversion techniques.