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Question from Grace:

What is non repeating decimal

Hi Grace,

A repeating decimal number is one that has a string of digits that repeats indefinitely. For example

where the digit 3 repeats indefinitely. The repeating pattern may contain more than 1 digit as in

587.67313131\cdot\cdot\cdot

where the pair of digits 31 repeats or

0.543254325432\cdot\cdot\cdot

where the pattern 5432 repeats.

A non-repeating decimal is one that is not a repeating decimal number. The examples that are usually given are \sqrt{2} and \pi, but it is reasonably easy to construct one yourself. For example

0.101001000100001\cdot\cdot\cdot

where the number of zeros between two ones continues to increase.

You might wonder why anyone cares if a decimal is repeating or not. The reason is that when you convert a common fraction \large \frac{a}{b} where a and b are integers, to decimal form by dividing the denominator into the numerator, the decimal is repeating. Try it with for example \large \frac{5}{7}.

The converse is also true, any repeating decimal can be expressed as a fraction. For example see our response to an earlier question.

Hence a non-repeating decimal number cannot be expressed as a common fraction.

I hope this helps,
Penny

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