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Math Help - non-repeating decimal

  1. #1
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    non-repeating decimal

    Can any non-repeating decimal be written as a fraction?


    For example, 0.21456456456456456
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by BlueStar View Post
    Can any non-repeating decimal be written as a fraction?


    For example, 0.21456456456456456...
    that is a repeating decimal. yes, it can be written as a fraction.

    NON-repeating decimals cannot be written as fractions, they are also known as irrational numbers. for instance, \sqrt {2}, \pi and e have NON-repeating decimal expansions, you cannot write them as fractions
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  3. #3
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    Quote Originally Posted by BlueStar View Post
    Can any non-repeating decimal be written as a fraction?

    For example, 0.21456456456456456
    Hello,

    provided that the ...456... is repeated endlessly then the decimal can be transformed into a fraction.

    Let x = 0.21456456456456...

    1. The non-repeating part contains 2 digits. Now multiply x by 10. You get:
    100x = 21.456456456456...

    2. The repeating part contains 3 digits. Now multipy the result of 1. by 10. You get:
    100000x = 21456.456456456456...

    3. Subtract both results:

    99900x = 21435. Solve for x: x=\frac{21435}{99900}=\frac{1429}{6660}
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