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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 Rip Rip Curl Offset Offset Curl BrownTan 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.


Offset Rip BrownTan Offset Curl Rip Curl 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 BrownTan Curl Offset Rip Rip Curl Offset 3

(c) 7.3656565... = 7.3 Offset BrownTan Curl Offset Rip Curl Rip 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

Rip Curl Offset Rip BrownTan Curl Offset Terminating Decimal

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Converting Decimals to Fractions

Converting Fractions to Decimals

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Repeating or Recurring Decimal

Pure Recurring Decimal

Curl Offset Offset Rip BrownTan Curl Rip Mixed Recurring Decimal

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PEMDAS Rules - Involving Integers

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PEMDAS Rule

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Conversion of Mixed Recurring Decimals into Vulgar Fractions

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Multiplying Decimal by a Decimal Number

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7th Grade Math Problems

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