Reduce a Decimal to
a Vulgar Fraction

Place,
for denominator, unity with as many ciphers after it as there are figures in the
numerator & reduce the fraction to its lowest terms.

Examples:

(1)
Reduce .875 to a vulgar fraction.

.

Macdonald
gives no further calculation. However, from earlier material in the notebook,
the greatest
common divisor between 875 and 1000 is 125. Dividing numerator and
denominator by 125 yields .

(2)
Reduce 25.84 to a vulgar fraction.

.

(3)
Reduce .265625 to a simple fraction.

.

As
in the other two examples, Macdonald gives no further calculation. Here are the
missing steps to get the greatest
common divisor between the numerator and the denominator:

1000000
= 3 × 265625 + 203125

265625
= 1 × 203125 + 62500

203125
= 3 × 62500 + 15625

62500
= 4 × 15625

Therefore
15625 is the greatest common divisor. Dividing 256625 and 1000000 by 15625
yields the given answer.