|
Calibration Resources
Fraction to Decimal Conversion Table
Important Note: any span of numbers that is underlined signifies that those numbers are repeated. For example, 0.09 signifies 0.090909....
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 precede 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 converted 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...
|
