I will provide a simple example. In decimal notation the number "five" is written as $5$, but in binary it is written as $101$ and in ternary as $12$. Same is the case for rational numbers. A …

Wikipedia claims that every repeating decimal represents a rational number. According to the following definition, how can we prove that fact? Definition: A number is rational if it can be writt...

Sep 5, 2011 · 43 I am trying to figure out how to prove that all rational numbers are either terminating decimal or repeating decimal numerals, but I am having a great difficulty in doing …

Jun 6, 2018 · On the other hand, $1/3$, being a fraction, is rational by definition, irrespective of any infinite repeating decimal sequence. The connection between irrational numbers and …

May 29, 2025 · When converting a repeating decimal into a fraction, the reason the denominator consists of 9s or a combination of 9s and 0s is rooted in the nature of the decimal system. …

We know that irrational numbers never repeat by combining the following two facts: every rational number has a repeating decimal expansion, and every number which has a repeating decimal …

Nov 19, 2024 · A repeating decimal is a rational number. Its value is (the repeating set of digits)/ (as many 9s as there are digits above). No, the product is a variable and whether or not it is …

Oct 22, 2020 · Do the trivial long division of 1 1 into x x. You will get remainder 0 0 each time, but the decimal sequence in the quotient need not be (eventually) repeating. Now, as for π π, it …

Detecting that a fraction is a repeating decimal Ask Question Asked 13 years, 3 months ago Modified 9 years, 6 months ago

Jan 8, 2025 · How do you change terminating but reapeating decimal into a fraction Example 0.88888? It is not possible to have a terminating decimal which repeats or a repeating decimal …