quotient.
EXERCISES.
Reduce to decimal fractions
½, ¼, ²/₂₅, ¹/₅₀, ³⁹²⁷/₁₂₅₀, and ⁴⁵³/₆₂₅.
Answer, ⁵/₁₀, ²⁵/₁₀₀, ⁸/₁₀₀, ²/₁₀₀, ³¹⁴¹⁶/₁₀₀₀₀, and ⁷²⁴⁸/₁₀₀₀₀.
- It will happen in most cases that the annexing of ciphers to the numerator will never make it divisible by the denominator without remainder. For example, try to reduce ¹/₇ to a decimal fraction.
- 7)1000000000000000000, &c.
- 142857142857142857, &c.
The quotient here is a continual repetition of the figures 1, 4, 2, 8, 5, 7, in the same order; therefore ¹/₇ cannot be reduced to a decimal fraction. But, nevertheless, if we take as a numerator any number of figures from the quotient 142857142857, &c., and as a denominator 1 followed by as many ciphers as were used in making that part of the quotient, we shall get a fraction which differs very little from ¹/₇, and which will differ still less from it if we put more figures in the numerator and more ciphers in the denominator.
Thus,
In the first column is a series of decimal fractions, which come nearer and nearer to ¹/₇, as the third