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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 Roxy II Roxy Roxy Jyll Jyll II BlackTan II BlackTan BlackTan Jyll Jyll II BlackTan Roxy 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.


Jyll Jyll II II Jyll BlackTan II Roxy Roxy Roxy BlackTan Roxy BlackTan BlackTan Jyll II 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 BlackTan II II BlackTan Roxy Jyll Jyll BlackTan Roxy Roxy BlackTan Roxy II II Jyll Jyll 3

(c) 7.3656565... = 7.3 Jyll BlackTan II Jyll Jyll Roxy Roxy Roxy Jyll BlackTan Roxy BlackTan BlackTan II II II 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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