# non-repeating decimal

• Jul 18th 2007, 08:38 PM
BlueStar
non-repeating decimal
Can any non-repeating decimal be written as a fraction?

For example, 0.21456456456456456
• Jul 18th 2007, 08:49 PM
Jhevon
Quote:

Originally Posted by BlueStar
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, $\displaystyle \sqrt {2}$, $\displaystyle \pi$ and $\displaystyle e$ have NON-repeating decimal expansions, you cannot write them as fractions
• Jul 18th 2007, 08:53 PM
earboth
Quote:

Originally Posted by BlueStar
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 10². You get:
100x = 21.456456456456...

2. The repeating part contains 3 digits. Now multipy the result of 1. by 10³. You get:
100000x = 21456.456456456456...

3. Subtract both results:

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