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 **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.

Calculating Non Terminating Decimals:

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

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.

Examples of mixed recurring decimals are:

(a) 3.1444... = 3.14(b) 8.12333... = 8.123

(c) 7.3656565... = 7.365

Solved examples on non-terminating decimal:

Find the decimal representation of 16/45.

**Solution:**

Using long division method, we get

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

● **Related Concept **

● Decimals

● Conversion of Unlike Decimals to Like Decimals

● Decimal and Fractional Expansion

● Converting Decimals to Fractions

● Converting Fractions to Decimals

● H.C.F. and L.C.M. of Decimals

● Repeating or Recurring Decimal

● BODMAS/PEMDAS Rules - Involving Decimals

● PEMDAS Rules - Involving Integers

● PEMDAS Rules - Involving Decimals

● BODMAS Rules - Involving Integers

● Conversion of Pure Recurring Decimal into Vulgar Fraction

● Conversion of Mixed Recurring Decimals into Vulgar Fractions

● Rounding Decimals to the Nearest Whole Number

● Rounding Decimals to the Nearest Tenths

● Rounding Decimals to the Nearest Hundredths

● Simplify Decimals Involving Addition and Subtraction Decimals

● 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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