Definition of Nonterminating 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 nonterminating decimal.
Note:
In some cases, a digit or a block of digits repeats itself in the decimal part. Such decimals are called nonterminating Flop BrownieLushOyster ShellSilver Showers Flip TKEES Duos repeating decimals or pure recurring decimals. These decimal numbers are represented by putting a bar on the repeated part.
Example of Nonterminating Decimal:
(a) 2.666... is a nonterminating repeating decimal and can be expressed as 2. 6.Flip BrownieLushOyster TKEES Flop ShellSilver Showers Duos 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 4Solved examples on nonterminating 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.
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