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 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.
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.
Examples of mixed recurring decimals are:(a) 3.1444... = 3.14
Solved examples on non-terminating decimal:
Find the decimal representation of 16/45.
Using long division method, we get
Therefore, 0.3555... = 0.35 and is a mixed recurring decimal.
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