&
-2
==

L T SO e
L 3 " aalaiiitidds i M E T L Ty L AR il L LT ey

116 THE FASCINATION OF NUMBERS

extract the integral part, if any, leaving a fractional part to
convert. The denominator is then divided by the numerator,
giving an integral answer plus a remainder. The remainder
is then used as a new divisor to divide into the previous
divisor, and this process is continued as far as required, a
note being made of the integer derived from each successive
division. These integers form the partial denominators of the
continued fraction.

It will be seen that this procedure is much the same as for
the calculation of the highest common factor of two numbers.
The fraction 2L is converted to a continued fraction as
shown:

521 ) 1023 ( 1
521
502 ) 521 ( 1
502
19) 502 ( 26

and is therefore equivalent to:

3 SRR b ey
I+1+264+242+142

This is a continued fraction for a rational expression and it
has a definite ending. A continued fraction for an irrational
expression is endless, and it depends upon the degree of
accuracy required as to how many terms are calculated. As