Make a Repeating Decimal Sign out of a Fraction
The repeating decimal sign, also called a vinculum, is a bar placed over decimal places that repeat indefinitely. For example, for 1/99 = 0.010101…, the three trailing periods indicate indefinite repetition of the 01. Instead, you can place a vinculum over the last 01 to indicate indefinite repetition. A fraction can be put into the repeating decimal form by performing long division of the fraction's denominator into its numerator. Or you can see the pattern by just using a calculator, if the repetition appears early enough.
Instructions
1. Set up the fraction for long division. Place a decimal point above the long-division bracket to line up with the decimal point of the numerator under the long-division bracket.
For example, the fraction 1/33 would be written with 33 on the left of the long-division bracket and 1. would be placed inside:
```_____
33)1.
2. Divide the denominator on the left into the numerator on the right as many whole (integer) times as possible. If this isn't possible an integral number of times, add a decimal place to the numerator and try again.
Continue with the example above. You have to change the 1 into 1.00 before you can divide 33 into it an integral number of times. So the first digit to appear above the 1.00 will be a 3, placed over the hundredths place. So it will read ".03" above the long-division bracket. Subtract 3 x 33 = 99 from the 100 to leave a remainder of 1.
```_____
33)1.00
___-99
_____1
(The underscores next to the 99 and 1 are here just as placeholders.)
3. Repeat step 2 until a pattern in the digits repeats. You'll find that the numbers in the arithmetic begin looping or repeating. They will be your proof that the pattern will continue indefinitely.
Continuing with the example above, the answer is .030303. The reason you know this will continue indefinitely is because the 33 to the left of the long-division bracket has to keep dividing into the number 100.
4. Place a line above the digits that are repeated to indicate indefinite repetition. This symbol is your "repeating decimal sign" or vinculum.
Continue with the example above. The answer .030303 would be written with a bar over the last 0 and the last 3.
Tags: long-division bracket, example above, indefinite repetition, indicate indefinite, indicate indefinite repetition, with example