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