the denominator. It appears that 1000 is divisible by 125, and that the quotient is 8. One cipher only has been annexed to the numerator, and therefore 100 divided by 125 is ·8. Had the fraction been ¹/₁₂₅, since 1000 divided by 125 gives 8, and three ciphers would have been annexed to the numerator, the fraction would have been
- Suppose that the given fraction has ciphers at the right of its denominator; for example, ³¹/₂₅₀₀. Then annexing a cipher to the numerator is the same thing as taking one away from the denominator; for, (108) ³¹⁰/₂₅₀₀ is the same thing as ³¹/₂₅₀, and ³¹⁰/₂₅₀ as ³¹/₂₅. The rule, therefore, is in this case: Take away the ciphers from the denominator.
EXERCISES.
Reduce the following fractions to decimal fractions:
| 1 | , | 36 | , | 297 | , and | 1 | . |
|---|---|---|---|---|---|---|---|
| 800 | 1250 | 64 | 128 | ||||
| Answer , ·00125, ·0288, 4·640625, | |||||||
| and | ·0078125. |
Find decimals of 6 places very near to the following fractions:
| 27 | , | 156 | , | 22 | , | 194 | , | 2637 | , | 1 | , | 1 | , and | 3 | . |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 49 | 33 | 37000 | 13 | 9907 | 2908 | 466 | 277 | ||||||||
| Answer , | ·551020, 4·727272, ·000594, 14·923076, ·266175, | ||||||||||||||
| ·000343, ·002145, and ·010830. |
- From (121) it appears, that if two fractions have the same denominator, the first may be divided by the second by dividing the numerator of the first by the numerator of the second.