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.
In some cases, a digit or a block of digits repeats itself in the decimal part. Such decimals are called non-terminating BlackBrown Roper BlackBrown BlackBrown Roper Roper Dusty Dusty Dusty Roper BlackBrown Dusty Roper BlackBrown Roper Dusty BlackBrown Dusty Roper 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.
Roper Dusty BlackBrown Roper Dusty Roper Dusty Dusty BlackBrown BlackBrown BlackBrown Dusty Roper Roper BlackBrown Dusty Roper BlackBrown Roper Calculating Non Terminating Decimals:
Using long division method, we will observe the steps in calculating 5/3.
• 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
Solved examples on non-terminating decimal:
Find the decimal representation of 16/45.
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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