Dave's Math Tables: Fraction to Decimal Conversion |
(Math | General | Arithmetic | Fraction to Decimal Conversion) |
Only fractions in lowest terms are listed.
For instance, to find 2/8, first simplify it to 1/4 then search for it
in the table below.
fraction = decimal | |||
1/1 = 1 | |||
1/2 = 0.5 | |||
1/3 = 0.3 | 2/3 = 0.6 | ||
1/4 = 0.25 | 3/4 = 0.75 | ||
1/5 = 0.2 | 2/5 = 0.4 | 3/5 = 0.6 | 4/5 = 0.8 |
1/6 = 0.16 | 5/6 = 0.83 | ||
1/7 = 0.142857 | 2/7 = 0.285714 | 3/7 = 0.428571 | 4/7 = 0.571428 |
5/7 = 0.714285 | 6/7 = 0.857142 | ||
1/8 = 0.125 | 3/8 = 0.375 | 5/8 = 0.625 | 7/8 = 0.875 |
1/9 = 0.1 | 2/9 = 0.2 | 4/9 = 0.4 | 5/9 = 0.5 |
7/9 = 0.7 | 8/9 = 0.8 | ||
1/10 = 0.1 | 3/10 = 0.3 | 7/10 = 0.7 | 9/10 = 0.9 |
1/11 = 0.09 | 2/11 = 0.18 | 3/11 = 0.27 | 4/11 = 0.36 |
5/11 = 0.45 | 6/11 = 0.54 | 7/11 = 0.63 | |
8/11 = 0.72 | 9/11 = 0.81 | 10/11 = 0.90 | |
1/12 = 0.083 | 5/12 = 0.416 | 7/12 = 0.583 | 11/12 = 0.916 |
1/16 = 0.0625 | 3/16 = 0.1875 | 5/16 = 0.3125 | 7/16 = 0.4375 |
11/16 = 0.6875 | 13/16 = 0.8125 | 15/16 = 0.9375 | |
1/32 = 0.03125 | 3/32 = 0.09375 | 5/32 = 0.15625 | 7/32 = 0.21875 |
9/32 = 0.28125 | 11/32 = 0.34375 | 13/32 = 0.40625 | |
15/32 = 0.46875 | 17/32 = 0.53125 | 19/32 = 0.59375 | |
21/32 = 0.65625 | 23/32 = 0.71875 | 25/32 = 0.78125 | |
27/32 = 0.84375 | 29/32 = 0.90625 | 31/32 = 0.96875 |
Need to convert a repeating decimal to a fraction? Follow these examples:
Note the following pattern for repeating decimals:
0.22222222... = 2/9
0.54545454... = 54/99
0.298298298... = 298/999
Division by 9's causes the repeating pattern.
Note the pattern if zeros preceed the repeating decimal:
0.022222222... = 2/90
0.00054545454... = 54/99000
0.00298298298... = 298/99900
Adding zero's to the denominator adds zero's before the repeating decimal.
To convert a decimal that begins with a non-repeating part, such as 0.21456456456456456..., to a fraction, write it as the sum of the non-repeating
part and the repeating part.
0.21 + 0.00456456456456456...
Next, convert each of these decimals to fractions. The first decimal has a
divisor of power ten. The second decimal (which repeats) is convirted according to the pattern
given above.
21/100 + 456/99900
Now add these fraction by expressing both with a common divisor
20979/99900 + 456/99900
and add.
21435/99900
Finally simplify it to lowest terms
1429/6660
and check on your calculator or with long division.
= 0.2145645645...