Next | Continued Fraction Arithmetic | 3 |

This includes paper calculation and also electronic calculation

The usual method is with a

*decimal expansion*Theorem: every real number

*r*has a unique representation as*a*_{0},*a*_{1},*a*_{2}...

*a*_{0}is any integer; 0 ≤*a*_{i}≤ 9 when*i*> 0For example:

173 / 2 =

`86 . 5 0 0 0 0 0 0`....1 / 3 =

`0 . 3 3 3 3 3 3 3 3 3 3`....1 0 / 7 =

`1 . 4 2 8 5 7 1 4 2 8 5 7`....=

`1 . 4 1 4 2 1 3 5`....π =

`3 . 1 4 1 5 9 2 6 5 3 5`....

(Actually, the representation is

*not quite*unique)(Since

`86 . 5 0 0 0 0 0 0`.... =`86 . 4 9 9 9 9 9 9`....)

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