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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 Cobian BlackTan Tica BlackTan Cobian BlackTan Tica BlackTan Cobian Tica Cobian Tica 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.


Cobian BlackTan BlackTan BlackTan Cobian Cobian BlackTan Cobian Tica Tica Tica Tica 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 Cobian Tica BlackTan Cobian BlackTan Tica Cobian Cobian Tica Tica BlackTan BlackTan 3

(c) 7.3656565... = 7.3 Tica Cobian BlackTan BlackTan Cobian Tica Cobian Cobian Tica BlackTan BlackTan Tica 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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Decimals

Decimal Numbers

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Decimal and Fractional Expansion

Cobian Cobian BlackTan Cobian Cobian Tica Tica BlackTan BlackTan BlackTan Tica Tica Terminating Decimal

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Converting Fractions to Decimals

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

Repeating or Recurring Decimal

Pure Recurring Decimal

BlackTan Cobian Tica BlackTan Tica Tica Cobian Cobian BlackTan Tica Cobian BlackTan Mixed Recurring Decimal

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Conversion of Mixed Recurring Decimals into Vulgar Fractions

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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