dividend to allow of this, annex ciphers to the beginning of it until there are. For example, divide 1734·229 by 1000: the decimal fraction is ¹⁷³⁴²²⁹/₁₀₀₀, which divided by 1000 (123) is ¹⁷³⁴²²⁹/₁₀₀₀₀₀₀, or 1·734229. If, in the same way, 1·2106 be divided by 10000, the result is
- Before proceeding to shorten the rule for the division of one decimal fraction by another, it will be necessary to resume what was said in (128) upon the reduction of any fraction to a decimal fraction. It was there shewn that ⁷/₁₆ is the same fraction as ⁴³⁷⁵/₁₀₀₀₀ or ·4375. As another example, convert ³/₁₂₈ into a decimal fraction. Follow the same process as in (128), thus:
- 128)300000000000(234375
- 256
- 440
- 384
- 560
- 512
- 480
- 384
- 960
- 896
- 640
- 640
- 0
Since 7 ciphers are used, it appears that 30000000 is the first of the series 30, 300, &c., which is divisible by 128; and therefore ³/₁₂₈ or, which is the same thing (108), ³⁰⁰⁰⁰⁰⁰⁰/₁₂₈₀₀₀₀₀₀₀ is equal to ²³⁴³⁷⁵/₁₀₀₀₀₀₀₀ or ·0234375 (135).
From these examples the rule for reducing a fraction to a decimal is: