| Fraction to Decimal Conversion |
| (Math | General | Fraction to Decimal Conversion) |
Fraction to Decimal Conversion Tables
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any span of numbers that is underlined signifies that those numbers are repeated. For example, 0.09 signifies 0.090909....Lillyview 1 4 15 Esv
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.
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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...
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As you may recall, a mixed number consists of an integer and a proper fraction. Any mixed number can also be written as an improper fraction, in which the numerator is larger than the denominator, as shown in the following example:
Example 1
To add mixed numbers, we first add the whole numbers together, and then the fractions.
If the sum of the fractions is an improper fraction, then we change it to a mixed number. Here's an example. The whole numbers, 3 and 1, sum to 4. The fractions, 2/5 and 3/5, add up to 5/5, or 1. Add the 1 to 4 to get the answer, which is 5.
Example 2
If the denominators of the fractions are different, then first find equivalent fractions with a common denominator before adding. For example, let's add 4 1/3 to 3 2/5. Using the techniques we've learned, you can find the least common denominator of 15. The answer is 7 11/15.
Subtracting mixed numbers is very similar to adding them. But what happens when the fractional part of the number you are subtracting is larger than the fractional part of the number you are subtracting from?
Here's an example: let's subtract 3 3/5 from 4 1/3. First you find the LCD; here it's 15.
Write both fractions as equivalent fractions with a denominator of 15. | |
3 + 1 5/15 - 3 9/15 3 + 20/15 - 3 9/15 | Since you're trying to subtract a larger fraction from a smaller one, you need to 'borrow' a one from the integer 4, change it to 15/15, and add it to the fraction. |
3 20/15 - 3 9/15 11/15 | Now the problem becomes 3 20/15 minus 3 9/15 and the answer is 11/15. |
