# Questions tagged [rational-numbers]

This challenge involves the manipulation of rational numbers, i.e. those which can be represented as a fraction of integers. Do not use this tag if rational numbers are just one of several admissible input/output formats, but rather if the use of exact rational arithmetic is required.

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### Repetend length in 1/n

This problem is based on non-terminating, repeating decimal points. Let $n$ be any positive integer $(n > 1 \text{ and } n < 10000)$, say $7$. Then, $1/n = 1/7 = 0.142857142857142857...$ ...
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### Diophantine Approximation: find lowest possible denominator to approximate within given precision

Challenge Given a number x and a precision e, find the lowest positive integer q such that <...
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### Cantor Function, Cruel

A ripoff of this challenge. Go upvote it! Objective Given a rational number amongst $[0,1]$, apply the Cantor function to it and output the rational number that's produced. The Cantor function The ...
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### Parse a Unicode vulgar fraction

Objective Given a string with single Unicode vulgar fraction, parse it to a rational number. Valid inputs A valid input is one of: ¼ U+00BC; one quarter ...
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### Convert a percentage to a “simple” ratio

You run a political website, and have determined that people have a better intuitive understanding when the chance of winning or losing an election is expressed as a ratio ("5 in 7") than when it is ...
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### Mixed Fraction Equality

In elementary school, children learn about proper fractions, where the numerator is less than the denominator, and thus the value of the fraction is less than one. Later, they are taught about ...
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### Exact Partial Sum of Harmonic Series

Challenge Given a positive integer N, output the sum of the first N reciprocals as an exact fraction, which is represented as a ...
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### Number the positive rationals

The positive rational numbers can be shown to be numerable with the following process: Zero has the ordinal 0 Arrange the other numbers in a grid so that row a, column b contains a/b Plot a diagonal ...
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### I want my book to be away from this table

Story So I have a book that I want to separate from my table with nothing but other books. I want to know how many books do I need to achieve this with $n$ book lengths. Here's a visualization ...
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### Delete the first periodic digit

We all know that whenever a rational number is written in decimal, the result is either terminating or (eventually) periodic. For example, when 41/42 is written in decimal, the result is ...
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### Bitwise XOR of rational numbers

Introduction Every rational number between 0 and 1 can be represented as an eventually periodic sequence of bits. For example, the binary representation of 11/40 is ...
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### Writing rational numbers as ratio of factorials of primes

Note: this challenge has been posted on the sandbox. Introduction This challenge is inspired by 2009 Putnam B1, a problem in an undergraduate mathematics competition. The problem is as follows: ...
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### Repeated reciprocal

What you need to do is create a function/program that takes a decimal as input, and outputs the result of repeatedly taking the reciprocal of the fractional part of the number, until the number ...
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### LCM of Rational Numbers

The least common multiple (LCM) of a set of numbers A is the smallest integer b such that b/a...
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Write a program or a function that takes two non-empty lists of the same length as input and does the following: uses elements of first list to get numerators, uses elements of the second list to get ...
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### Infinitely Print Zeno's Dichotomy Paradox (1/(2^n))

Wikipedia: Zeno's Dichotomy Paradox An infinite number of mathematicians walk into a bar. The first one orders a beer. The second one orders half a beer. The third one orders a fourth of a beer. The ...
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### Rational decomposition a = xyz(x+y+z)

Write functions x(a), y(a) and z(a) such that for any rational ...
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### The Imperial Ruler

Given a ruler length in inches and fractions of an inch, and a granularity in fractions of an inch, output the values of all marks on the ruler, starting from 0, in ascending order. Input ruler length ...
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### Fraction Frenzy!

EDIT: I'm getting a lot of comments about this not terminating - I will give the "correct answer" tag to either the first person who gives me FF(3) (as in provides ...
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### Is it within the Cantor set?

The Challenge For this challenge, you are supposed to determine if a given number is in the Cantor set. So first, let's define the Cantor set. First, start with the numbers between 0 and 1. Any ...
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### Swap out some periodic and non-periodic parts

In the decimal representation of every rational number p/q, you have a periodic tail, a non-periodic head, and a section before the decimal point in the following ...
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### Golfed decimal fractions

Your goal is to write some code that will output the shortest unique decimal sequence for the input fraction. No two fractions with the same denominator may have the same output, although it's ...
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### The nth numerator

You can create a list of all rationals 0 < r ≤ 1 by listing them ordered first by denominator and then by numerator: ...
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### Simplify a continued fraction

Continued fractions are expressions that describe fractions iteratively. They can be represented graphically: Or they can be represented as a list of values: ...
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### Output the nth rational number according to the Stern-Brocot sequence

The Stern-Brocot sequence is a Fibonnaci-like sequence which can be constructed as follows: Initialise the sequence with s(1) = s(2) = 1 Set counter ...
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### Fraction to exact decimal

Write a program or function that given two integers a, b outputs a string containing a decimal number representing the fraction a/b exactly. If a/b is integer, simply output the value, without a ...
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### Continued Fraction of a Rational Number

The continued fraction of a number n is a fraction of the following form: which converges to n. The sequence ...
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### Calculate the Gamma function for half-integer arguments

Gamma function is defined as It is a well-known fact that for positive integers it coincides with a properly shifted factorial function: Γ(n) = (n - 1)!. However, ...
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### In-between fractions

In-between fractions The challenge: You will need to create code that takes atleast 3 inputs; 2 integers and "a fraction representation" - whichever type suits your language for representing the ...
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### Solve a quadratic equation using Vieta's formulas

Exposition Your mathematics teacher is a big fan of Vieta's formulas, and he believes that you should use them to solve quadratic equations. Given the equation ...
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### Can a fraction be simplified using Anomalous Cancellation?

Anomalous Cancellation (from Wolfram Alpha): Anomalous cancellation is a "canceling" of digits of a and b in the numerator and denominator of a fraction a/b which results in a fraction equal to the ...
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### Mixed Number to an Improper Fraction

Mixed Number to an Improper Fraction In this challenge you will be converting a mixed number to an improper fraction. Because improper fractions use fewer numbers, your code will need to be as short ...
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### When Bullets Collide

This challenge is based off a riddle I read in some book a while ago, which I found again here. It is about bullets fired from a gun once per second at varying speeds that travel in a straight line ...
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### Calculate the p-adic norm of a rational number

Calculate the p-adic norm of a rational number Write a function or a program, that takes 3 integers m,n,p (where p is a ...
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### Lookalike shapes

Similar figures Two rectangles are similar if the ratios of their sides are the same. Consider these two rectangles; a rectangle 5 lines tall and 11 chars wide: ...
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### World Big Dosa​

You are a talented young chef who has just been offered the position of sous chef at the world's most prestigious Indian restaurant. You have little experience with preparing Indian cuisine, but you'...
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### Calculate a probability exactly

This task is about writing code to compute a probability exactly. The output should be a precise probability written as a fraction in its most reduced form. That is it should never output ...
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### XKCD Bracket Probabilities

Today's XKCD is a sports-tournament style bracket, where the contestants are well-known names, put into groups of possibly confusing names. Give the probability that a given contestant will win the ...