Repeating or Recurring Decimal

Definition of Recurring Decimal:

Recurring decimal is also known as repeating decimal. In a decimal, a digit or a sequence of digits in the decimal part keeps repeating itself infinitely. Such decimals are called non-terminating repeating decimals or recurring decimals.

More information about Repeating or Recurring Decimal:

The repeating decimal can be expressed by putting a bar over the digit or on the repeated digits that repeat itself.

Also, dot can be put over the first and the last digit of the repeated block.

A few worked-out problems are explained here with step-by-step explanation to understand how to calculate or find repeating or recurring decimal.

Examples of Recurring Decimal:

(a) 17/45

Recurring Decimals

= 0.3777…….

For, 17/45 when 17 is divided by 45, the quotient is 0.3777.... and the digit 7 is repeating.

For instance, 0.377777777777......... can also be written as 0.37

Alternatively, we can write it by placing a dot above the repeating digit 7 in the quotient.

Repeating Decimal Sign

Therefore, 17/45 is a repeating decimal.

(b) 1/3

Repeating Decimals

= 0.333.........

For, 1/3 when 1 is divided by 3, the quotient is 0.333..... and the digit 3 is repeating.

For instance, 0.33333333......... can also be written as 0.3

Alternatively, we can write it by placing a dot above the repeating digit 3 in the quotient.

Repeating Decimal Notation

Therefore, 1/3 is a repeating decimal.

(c) 2/11

Examples of Recurring Decimal

= 0.1818

For, 2/11 when 2 is divided by 11, the quotient is 0.1818..... and the digits 18 are repeating.

For instance, 0.181818......... can also be written as 0.18

Alternatively, we can write it by placing a dot above the repeating digits 18 in the quotient.

Recurring Decimal Notation

Therefore, 2/11 is a repeating decimal.

Related Concept


Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

● Conversion of Pure Recurring Decimal into Vulgar Fraction

● Conversion of Mixed Recurring Decimals into Vulgar Fractions

7th Grade Math Problems

From Repeating or Recurring Decimal to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Share this page: What’s this?

Recent Articles

  1. Tangrams Math | Traditional Chinese Geometrical Puzzle | Triangles

    Apr 17, 24 01:53 PM

    Tangram is a traditional Chinese geometrical puzzle with 7 pieces (1 parallelogram, 1 square and 5 triangles) that can be arranged to match any particular design. In the given figure, it consists of o…

    Read More

  2. Time Duration |How to Calculate the Time Duration (in Hours & Minutes)

    Apr 17, 24 01:32 PM

    Duration of Time
    We will learn how to calculate the time duration in minutes and in hours. Time Duration (in minutes) Ron and Clara play badminton every evening. Yesterday, their game started at 5 : 15 p.m.

    Read More

  3. Worksheet on Third Grade Geometrical Shapes | Questions on Geometry

    Apr 16, 24 02:00 AM

    Worksheet on Geometrical Shapes
    Practice the math worksheet on third grade geometrical shapes. The questions will help the students to get prepared for the third grade geometry test. 1. Name the types of surfaces that you know. 2. W…

    Read More

  4. 4th Grade Mental Math on Factors and Multiples |Worksheet with Answers

    Apr 16, 24 01:15 AM

    In 4th grade mental math on factors and multiples students can practice different questions on prime numbers, properties of prime numbers, factors, properties of factors, even numbers, odd numbers, pr…

    Read More

  5. Worksheet on Factors and Multiples | Find the Missing Factors | Answer

    Apr 15, 24 11:30 PM

    Worksheet on Factors and Multiples
    Practice the questions given in the worksheet on factors and multiples. 1. Find out the even numbers. 27, 36, 48, 125, 360, 453, 518, 423, 54, 58, 917, 186, 423, 928, 358 2. Find out the odd numbers.

    Read More