is it possible to turn a recurring decimal into a terminating decimal

Expert Answers
justaguide eNotes educator| Certified Educator

A recurring decimal number cannot be written as on with a terminating decimal. If a recurring number is written as one with a terminating decimal there is a loss in accuracy.

The number would have to be rounded off to the required number of decimal places. The rules for rounding numbers would be applicable when writing a recurring decimal number as on with a limited number of decimal numbers. For example, 1/3 = 0.333333... could be written as 0.33 and 2/3 = 0.666... could be written as 0.67 if there are only 2 significant decimal numbers in both the cases.

etotheeyepi | Student

I need to correct one thing.  I'm not sure how to say it correctly.

Any fraction in the series 1/2, 1/4, 1/8 ... is a terminating decimal, 

etotheeyepi | Student

I suppose a bit of rebuttal will help.  Any number can be written as a terminating decimal, if one is willing to write the number in a number system, which has the number as a factor.  In base 2 only 1/2 is a terminating decimal.

Three is a factor of 60, so 1/3 in base 60 might be written 0.20 because 20 is 1/3 of 60.  

In practical terms, 1/3 of an hour is 20 minutes.

etotheeyepi | Student

In the base ten number system 1/2, 1/4, 1/5, and 1/10 are terminating decimals.   The fractions 1/3, 1/6, and 1/12 are repeating decimals.

If you write all the numbers in the base 60 number system, all of the above fractions are terminating decimals.