Why is a repeating decimal a rational number?
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 fraction like …
number systems - Proof that every repeating decimal is rational ...
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...
Why is pi non-repeating? - Mathematics Stack Exchange
Oct 22, 2020 · This is the very definition of what it means for a number to be rational. And indeed your argument is a correct proof that the decimal representation of any rational number repeats. But $\pi$ …
When you write a repeating decimal into a fraction why does the ...
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. Each digit …
How can I prove that all rational numbers are either terminating ...
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 so. Any help will be …
education - How to know that irrational numbers never repeat ...
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 …
Why aren't repeating decimals irrational but something like $\pi$ is?
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 decimal …
real analysis - Is a non-repeating and non-terminating decimal always ...
An irrational number has a non-terminating, non-repeating decimal expansion. So there is no real idea of closeness here, unless you are talking about distance, ($\epsilon$ close), in which case yes you are …
The longest repeating decimal that can be created from a simple ...
Nov 30, 2019 · 10 What's the longest possible repeating decimal (repetend) that can be created from a fraction if: The numerator has to be less than or equal to 9,999 The denominator has be less than or …
How do you convert a repeating decimal into percent? - Answers
Apr 28, 2022 · What is .5 repeating as a percent? Ah, a happy little question! When we have a decimal that repeats, like 0.5 with the 5 repeating, we can convert it to a percent by multiplying it by 100. So, …