Converting Non Terminating Repeating Decimals into Fractions


 
 
Concept Explanation
 

Converting Non Terminating Repeating Decimals into Fractions

Non Terminating Repeating Decimals:

The rational numbers which when expressed in decimal form by division method, no matter how long they are divided, they always leave a remainder . In other words, the division process never comes to an end. This is due to the reason that in the division process the remainder starts repeating after a certain number of steps. In such cases, a digit or a block of digits repeats itself.For example, 0.3333...,0.1666666....,0.123123123....,1.2692307692307692307.... etc. Such decimals are called non-terminating repeating or recurring decimals. These decimal numbers are represented by putting a bar over the first block of the repeating part and omit the other repeating blocks.

Thus, we write

 0.33333 ...= 0.bar{3},

0.16666... =0.1overline{6}

0.123123123 .. =0.overline{123} and

1.26923076923076292307 ... =1.2overline{692307}.

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Sample Questions
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Question : 1

Express large overline{0.001} as a fraction in the simplest form.

Right Option : D
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Question : 2

Express the following decimals in the form frac{p}{q}: large 0.003overline{52}

Right Option : B
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Explanation
Question : 3

Express each of the following decimals in the form LARGE frac{p}{q}   :    large 0.bar{4}

Right Option : B
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Explanation
 
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