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Definition of Non-terminating Decimal:

While expressing a fraction in the decimal form, when we perform division we get some remainder. If the division process does not end i.e. we do not get the remainder equal to zero; then such decimal is known as non-terminating decimal.

Note:

In some cases, a digit or a block of digits repeats itself in the decimal part. Such decimals are called non-terminating MIA Tina MIA BlackGrayRed BlackGrayRed Tina MIA Tina BlackGrayRed repeating decimals or pure recurring decimals. These decimal numbers are represented by putting a bar on the repeated part.


Example of Non-terminating Decimal:

(a) 2.666... is a non-terminating repeating decimal and can be expressed as 2. 6.

(b) 0.141414 ... is a non-terminating repeating decimal and can be expressed as 0. 14.


MIA Tina BlackGrayRed BlackGrayRed BlackGrayRed Tina MIA MIA Tina Calculating Non Terminating Decimals:

Using long division method, we will observe the steps in calculating 5/3.




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Therefore, 1.666... is a non-terminating repeating decimal and can be expressed as 1. 6.

In some cases at least one of the digits after the decimal point is not repeated and some digit/digits are repeated, such decimals are called mixed recurring decimals.


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Examples of mixed recurring decimals are:

(a) 3.1444... = 3.1 4

(b) 8.12333... = 8.12 BlackGrayRed BlackGrayRed MIA Tina MIA Tina Tina MIA BlackGrayRed 3

(c) 7.3656565... = 7.3 MIA Tina MIA Tina Tina BlackGrayRed BlackGrayRed BlackGrayRed MIA 65


Solved examples on non-terminating decimal:

Find the decimal representation of 16/45.

Solution:

Using long division method, we get








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Therefore, 0.3555... = 0.35 and is a mixed recurring decimal.

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Decimal and Fractional Expansion

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Converting Decimals to Fractions

Converting Fractions to Decimals

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

Repeating or Recurring Decimal

Pure Recurring Decimal

Tina MIA BlackGrayRed MIA MIA BlackGrayRed Tina Tina BlackGrayRed Mixed Recurring Decimal

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PEMDAS Rules - Involving Integers

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PEMDAS Rule

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Conversion of Pure Recurring Decimal into Vulgar Fraction

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Simplification of Decimal

Rounding Decimals

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Multiplying Decimal by a Decimal Number

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7th Grade Math Problems

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