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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 Saylor Saylor BlackTan Roxy Roxy Roxy Saylor BlackTan BlackTan 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.


Saylor BlackTan Roxy Roxy BlackTan Roxy Saylor Saylor BlackTan 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 Saylor Saylor Saylor Roxy Roxy Roxy BlackTan BlackTan BlackTan 3

(c) 7.3656565... = 7.3 Saylor Saylor Roxy Roxy BlackTan Saylor Roxy BlackTan BlackTan 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

Decimal Fractions

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Comparing Decimals

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Decimal and Fractional Expansion

BlackTan BlackTan Saylor Roxy Saylor Roxy BlackTan Saylor Roxy Terminating Decimal

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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

Roxy BlackTan Roxy Saylor BlackTan BlackTan Saylor Saylor Roxy Mixed Recurring Decimal

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PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

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Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

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Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number


7th Grade Math Problems

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