Example: Express 332 as a decimal.
| 4 | ) | 3 | .0 | |
| 8 | ) | .75 | ||
| .09375 | Ans. | |||
It will be found in many cases that there is always a remainder, so that the quotient can be continued indefinitely.
Circulating Decimals
The learner has already discovered that some common fractions cannot be changed to exact decimal fractions, as—
1⁄3 =.33333 on to infinity.
2⁄3 =.66666 on to infinity.
7⁄33 =.212121, etc.
These decimals are known as Circulates, Recurring or Circulating decimals.
The part which recurs is called the Repetend.
This is marked by putting a dot over the first and last figures of it. For instance, if we write the 21 in the last case above, this way: 2̊1̊, it indicates that, if written out, the result would be 21212121, etc., on to infinity.
Where a circulating decimal occurs in work, it is best to reduce it to a common fraction. If need be, it may be expressed in the result as a circulate to any number of decimal places.