Become a math whiz with AI Tutoring, Practice Questions & more.

HotmathMath Homework. Do It Faster, Learn It Better.

Terminating and Repeating Decimals

Any rational number (that is, a fraction in lowest terms) can be written as either a terminating decimal or a repeating decimal . Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.

Example 1:

Convert the fraction 5 8 to a decimal.

The division is as follows:

0.625 8 5.000 48 _ 20 16 _ 40 40 _ 0

So, 5 8 = 0.625 . This is a terminating decimal.

Example 2:

Convert the fraction 7 12 to a decimal.

The division is as follows:

0.5833 12 7.0000 6 0 _ 1 00 96 _ 40 36 _ 40 36 _ 4

So:

7 12 = 0.58 3 ¯

This is a repeating decimal.

The bar over the number, in this case 3 , indicates the number or block of numbers that repeat unendingly.

See also Converting Repeating Decimals to Fractions .

 

Subjects Near Me
Popular Cities
Popular Subjects
;
Download our free learning tools apps and test prep books
varsity tutors app storevarsity tutors google play storevarsity tutors amazon storevarsity tutors ibooks store