I am confused about the information content of exact decimal representations of rational fractions (a whole number divided by another whole number). Some, such as ¼ are finite (0.25), some, infinite 1/3 =0.33333…The example: 93/104, has a lead in of 3 digits then an infinitely repeated sequence of 6 digits: 0.894[230769] [230769] ….; while 93/108 = 0.86[1][1]….; Division by a prime number has no lead in, only an infinitely repeated sequence eg for 93/107 the sequence is 53 digits, while 93/113 has a 112 digit sequence, (which is the maximum possible length of the repeat sequence = denominator -1). It seems different amounts of information are required to exactly specify each of these apparently similar fractions. Is this so? or do they have the same information content but some are more “compressible”, contrasting with irrational fractions which are not “compressible” at all?
2026-04-03 16:23:19.1775233399
information and rational fractions
43 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ELEMENTARY-NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- How do I show that if $\boldsymbol{a_1 a_2 a_3\cdots a_n \mid k}$ then each variable divides $\boldsymbol k $?
- Using only the digits 2,3,9, how many six-digit numbers can be formed which are divisible by 6?
- Algebra Proof including relative primes.
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
- algebraic integers of $x^4 -10x^2 +1$
- What exactly is the definition of Carmichael numbers?
- Number of divisors 888,888.
Related Questions in INFORMATION-THEORY
- KL divergence between two multivariate Bernoulli distribution
- convexity of mutual information-like function
- Maximizing a mutual information w.r.t. (i.i.d.) variation of the channel.
- Probability of a block error of the (N, K) Hamming code used for a binary symmetric channel.
- Kac Lemma for Ergodic Stationary Process
- Encryption with $|K| = |P| = |C| = 1$ is perfectly secure?
- How to maximise the difference between entropy and expected length of an Huffman code?
- Number of codes with max codeword length over an alphabet
- Aggregating information and bayesian information
- Compactness of the Gaussian random variable distribution as a statistical manifold?
Related Questions in RATIONAL-NUMBERS
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- I don't understand why my college algebra book is picking when to multiply factors
- Non-galois real extensions of $\mathbb Q$
- A variation of the argument to prove that $\{m/n:n \text{ is odd },n,m \in \mathbb{Z}\}$ is a PID
- Almost have a group law: $(x,y)*(a,b) = (xa + yb, xb + ya)$ with rational components.
- When are $\alpha$ and $\cos\alpha$ both rational?
- What is the decimal form of 1/299,792,458
- Proving that the sequence $\{\frac{3n+5}{2n+6}\}$ is Cauchy.
- Is this a valid proof? If $a$ and $b$ are rational, $a^b$ is rational.
- What is the identity element for the subgroup $H=\{a+b\sqrt{2}:a,b\in\mathbb{Q},\text{$a$ and $b$ are not both zero}\}$ of the group $\mathbb{R}^*$?
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?