not be visible to the eye. Therefore, in finding a length, an error of a ten-millionth part of an inch is of no consequence, even where the finest measurement is necessary. Now, by carrying on the table in (129), we shall see
| 1428571 | does not differ from | 1 | by | 1 | ; |
|---|---|---|---|---|---|
| 10000000 | 7 | 10000000 |
and if these fractions represented parts of an inch, the first might be used for the second, since the difference is not perceptible. In applying arithmetic to practice, nothing can be measured so accurately as to be represented in numbers without any error whatever, whether it be length, weight, or any other species of magnitude. It is therefore unnecessary to use any other than decimal fractions, since, by means of them, any quantity may be represented with as much correctness as by any other method.
EXERCISES.
Find decimal fractions which do not differ from the following fractions by ¹/₁₀₀₀₀₀₀₀₀.
| ⅓ | Answer , | ³³³³³³³³/₁₀₀₀₀₀₀₀₀. |
|---|---|---|
| ⁴/₇ | ⁵⁷¹⁴²⁸⁵⁷/₁₀₀₀₀₀₀₀₀. | |
| ¹¹³/₃₅₅ | ³¹⁸³⁰⁹⁸⁵/₁₀₀₀₀₀₀₀₀. | |
| ³⁵⁵/₁₁₃ | ³¹⁴¹⁵⁹²⁹²/₁₀₀₀₀₀₀₀₀. |
- Every decimal may be immediately reduced to a quantity consisting either of a whole number and more simple decimals, or of more simple decimals alone, having one figure only in each of the numerators. Take, for example,