Question

The decimal 0.3 repeat represents 1/3. What the of number best describes 0.9 repeat, which is 3x0.3 repeat? Explain

Answer 1

0.9 repeat is not 1. 0.999, nor .9999999999 are not equal to 1. If the expansion of 9’s is stopped at any finite point, the resulting fraction (for example, 0.9999 = 9,999/10,000) will never be equal to 1. Each time a 9 is added, the error decreases, but will not take the number to 1. With each 9 added, the error becomes ten times smaller. The is no number that the sequence of 9’s gets arbitrarily close to. The error would look like 1/infinity, however, it is more precise to say that the limit of the sequence is zero.