Questions on the different ways to represent a number, how to convert between those different ways, and other such questions. The usual system employed by humans is the decimal (base-10) system, but other systems like binary and hexadecimal are also in frequent use.

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How do I efficiently budget for digits when converting from one base to another?

I'm trying to work out a formula that gives me the minimum number of digits required to express a number in a target radix (r2) knowing only the source radix (r1) and number of significant digits (d). ...
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0answers
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In Roman System, what does it mean that S1 cannot be before S2 if S1<=S2*10?

My textbook(Foundations of Computer Science - Cengage Learning) says "A symbol S1 cannot come before another symbol S2 if S1 <= 10 * S2. For example, I or V cannot come before C." If ...
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1answer
22 views

Converting double precision IEEE 754 hex to base 10 with repeating decimals

The number is 0x4001 8CCC CCCC CCCC. So far I have the stored exponent as 1000000000 which equals ...
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1answer
48 views

Numerals vs. Numbers

I've noticed three different approaches in general use: Numbers are abstract and numerals are used to express numbers following a particular set of rules. The number of days in two weeks is a ...
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1answer
64 views

Systematic way to represent any irrational number

I'm wondering if there's a way to symbolically (or is there a more lose constraint?) represent ANY irrational number in a systematic way. You can represent any rational number as two integers and I ...
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2answers
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Base 4 Mathematics

I have an homework question but I'm having hard time to understand the context. Here is the question: Assume that you are using 3-digit number system with base r = 4 (and n = 3). Assume also ...
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2answers
12 views

query regarding number systems [closed]

how should i convert huge decimal number quickly to binary number using pen and paper?
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1answer
71 views

Are the quaternions obsolete in pure mathematics?

I remember I read an article saying that "The quaternions $\Bbb{H}$ are obsolete in pure mathematics since the theory of vectors has been developed enough, however it is useful in computer science". ...
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1answer
25 views

How do I detect whether a rational number has a repetend when expressed with a different radix?

My original and basic question is: How do I detect whether a rational number has a repetend when expressed with a different radix? Here is my question restated as an example: Given ...
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If I were to define a new system of numbers in the 3rd dimension, what do I need to do?

I am currently working on defining a new set of numbers called kenosymplirostic which defines x/0 as xk where k is the kenosymplirostic unit equal to 1/0. Full detail is in this page: Kenosymplirostic ...
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0answers
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Is multiplication in mixed radix numeral systems complicated?

The wikipedia article on mixed radix numeral systems says Mixed-radix numbers of the same base can be manipulated using a generalization of manual arithmetic algorithms. This sounds like "naive ...
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1answer
23 views

Determine the $n$th string among those of a given length in alphabetical order starting at a given string and using a given character set?

When building strings using a particular character set (the set can change), such as in a brute-force password cracking, how would I determine which string occurs in the $n$th position when the ...
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1answer
29 views

Is there a conventional symbol for the set of radical expressions?

There is already a question about the name of such a set: Name for numbers expressible as radicals My question is related. The rational complex numbers might be denoted ℚ(i), and the algebraic ...
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0answers
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Is there a conventional symbol for the set of real algebraic numbers?

The real numbers are denoted ℝ, and the algebraic numbers are conventionally denoted 𝔸. Is there such convention for the real algebraic numbers ℝ∩𝔸?
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10answers
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Can a number have infinitely many digits before the decimal point?

I asked my teacher if a number can have infinitely many digits before the decimal point. He said that this isn't possible, even though there are numbers with infinitely many digits after the decimal ...
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1answer
40 views

Finding which base number given operations

$$ (35_a + 24_a) * 21_a = 1081_a $$ Which base is the above number? Any advice on how to solve questions like these? I tried making it in to a polynomial: $(3a+5 + 2a+4) * (2a+1) = 108a + 1$ ...
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0answers
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How many rationals for a given $n \in \Bbb N \;\backslash \{1\}$?

Fix $n \in \Bbb N, n> 1$. Now choose a two digit base-$n$ number $ab $ say. There's $n^2$ choices for this. Consider the number $0.c_1 c_2 c_3 \ldots$ where the $c_i$ are defined recursively: ...
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1answer
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Fractional parts in base number systems other than base-10?

A long-standing question I've asked myself over and over again is how one might express fractional parts of a whole in base number systems other than 10. Is it truly as simple as base-10's x/y system? ...
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2answers
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Represent non-integer values on the factorial base

I want to compute the representation of the following values using the factorial number system: $\pi$ $e$ $\phi$ I know how to do it for integer values, but is it feasible for non-integer values? ...
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1answer
38 views

Are there any number systems better suited to nature?

For example, number such as $\pi$ and $e$ cannot be represented as rational numbers in our number study and extend in decimal places to infinity. QUESTION: Is there a possibility that some other ...
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How to express the quantity using significant figures to imply the stated error?

Express the quantity using significant figures to imply the stated error. $$1.77 \pm 0.06$$ I tried to factor out a $6$ and got $6(.295\pm0.01)$ but then when I try to make $.295$ have an error of ...
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1answer
28 views

Using significant figures to express stated errors?

The question reads, " express each of the following quantities using significant figures to imply the stated error". a) $2.3 \pm 0.001$ b) $1.989 \pm 0.0003$ I think the first one is 2.300 because ...
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1answer
44 views

What is the numeral system which uses the number of digits as a signifier of value called?

Our standard notation of representing numbers has an implied infinite number of zero digits on the left of all numbers. 42, 042 and 00000000042 all represent the same number. I'm thinking of the ...
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1answer
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Why $0.999$… isn't the largest number before 1? [duplicate]

Why doesn't it called like that? It seems fair, $1$ called $1$ while $0.999$... being the largest number before $1$, and not called $1$ while not look like it is. Let's say it isn't, how would that ...
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0answers
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Roman Numerals. What are valid Subtractives? e.g. Is VL valid for 45?

"Standard" syntax for Roman Numerals seem to always show 45 = XLV. I wrote a little program to convert roman numerals to integers, so I started wondering what is valid in subtractive notation and ...
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0answers
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Ternary balance with unknown weight

Main references: Ternary (Wolfram MathWorld) Balanced ternary (Wikipedia) Weighing scale: Balance (Wikipedia) <quote> Balanced ternary has other applications besides computing. For example, a ...
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1answer
58 views

Given the normalised floating point number system, calculate smallest possible value of y - x

First I present the problem and then my workings and thoughts: Given the normalized floating point number system $(\beta, t, L, U) = (10, 7, -6, 4)$ where $\beta$ is the base and $t$ is the ...
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2answers
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For any base-$n$ number system, what is the average length of a number $\leq100$?

By this I mean the amount of symbols (bits / digits / etc. ) for any number from $0$ to $100$. I don't know whether this can be answered, I'm just asking out of interest - not homework or anything.
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4answers
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How to compute 1/7 in base 8?

This is probably a very basic question but nonetheless I choked when I got in a math for programmers class. I was taught how to convert from base to base but I have no idea how to convert fractions to ...
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1answer
26 views

Conversion in Number system

Here I provide the image. My question is why is it necessary to have 2 different results of the same problem. Am I doing something wrong. Please Help! Thanks in advance.
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1answer
38 views

Two conversions to base three yield different results

How are there two different conversion results for the same bases? Am I doing something wrong?
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0answers
28 views

number of trailing zeroes of factorial raise to power by another factorial

Finding trailing zeroes in any factorial is easy. Every time you pass a multiple of 10 (or something 5 mod 10) you will accumulate another 0 For example 10! has two trailing zeros, one from ...
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1answer
67 views

Calculating a Factorial Base Representation

My friend thought of a system in which each number $n$ (I will first restrict my question to positive integers $n$) is represented by a digit string $(d_l,...,d_1)$ as follows $\forall n \in ...
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1answer
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Absolute and relative error of a binary number?

Given is the following system $A:={ \pm 1.a_1 a_2 a_3 a_4 \cdot 2^e}$, $a_{i}\in \left \{ 0,1 \right \}$, $i\in \left \{ 1,2,3,4 \right \}$, $e\in \left \{ -8,\ldots,8 \right \}$. Find the absolute ...
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4answers
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About a specific argument purporting to show $0.999\dots = 1.0$.

I have read the proofs about why $0.9999.... = 1$, which are satisfying. But I can't get the following argument out of my head. Defining $0.9999....$ : Lets construct a non-terminating but recurring ...
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1answer
958 views

What is fleventy five?

In an episode of "Silicon Valley", one of the characters goes on a rant about how smart he is and cut his teeth on 'hex tables', and he says, "ask me what F times 9 is. It's fleventy-five!" This is ...
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1answer
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Were there attempts to build a system of numbers where division by a negative number is greater than division by any positive number?

When we decrease the positive denomenator of a ratio (with positive numerator), the value of the ratio increases. The same happens for negative denomenators. But in zero this law is broken. Were there ...
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1answer
344 views

Finding a rational number which is simply normal to relatively prime bases

Let $n\ge 2\in\mathbb Z$. Suppose that a base-$n$-decimal $(0.a_1a_2a_3\cdots)_n$ represents $\sum_{k=1}^{\infty}\frac{a_k}{n^k}$ where $a_{i}\in\{0,1,\cdots,n-1\}\ (i=1,2,\cdots)$ is each digit ...
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1answer
39 views

Converting a repeating base $7$ expression to a fraction

A question was given to me to convert a decimal in base seven to a fraction in base seven, where the base $7$ expression was $._7515151515\ldots$. I understand this would be $\frac 57 + \frac 1{49} + ...
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1answer
46 views

Can we construct a number system in which **all** (uni-variable) equations can be solved?

$\mathbb{C}$ is nice and safe, in that it's algebraically closed, so we can solve all polynomials in $\mathbb{C}$, but there are still equations that cannot be solved in this set. I'm wondering: ...
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1answer
25 views

How to show that for any $n\in\Bbb N\;,n^+=n+1$

Show that for Any $n\in\Bbb N\;,n^+=n+1$ We know for $ n=0 , 0^+=1+0$ for $n\in\Bbb N$ supposing that $n^+=1+n$ then have to show $(n+1)^+=n+1+1=n^++1$
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2answers
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between 1-2 there comes 1.1,1.2,1.333,1.679,1.999999 etc So what we crossed to get '2' [closed]

If there are infinite numbers between 2 real numbers, then what number we actually cross to get the next number. eg. between 1-2 there comes 1.1,1.2,1.333,1.679,1.999999 etc So what we crossed to get ...
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3answers
182 views

Arrange four nine and two symbol to make total of $100$?

Can you arrange four $9$'s and use of at most $2$ math symbols , make the total be $100$? Is this really possible? If it is possible can you help me out?
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1answer
84 views

Prove that in any base the number of digits composing the repetitive mantissa of the reciprocal of a prime $p$ never exceeds $p-1$.

I was trying to find bases where the reciprocals of primes have a short repetitive mantissa. Here is what I found: http://imagizer.imageshack.us/a/img835/7738/c7gb.png The bases are on the left. The ...
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3answers
197 views

How do I add multiple binary numbers without using a partial sum?

I know how to add binary numbers but what I normally do is add the first 2 binary numbers and then add the 3rd one to their sum. It is really slow. $$ 111_2 + 111_2 + 111_2 + 111_2 $$ Here is ...
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0answers
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Name for numbers with a single non-zero digit.

Given a base, is there a name for the numbers (positive or negative) that have only a single non-zero digit? For example: Decimal: 4000, -30, 0.0008 Binary: 1000 Base 5: 300, -0.1 Contrived ...
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2answers
50 views

Using Euclid's Algorithm prove..

Using Euclid's Algorithm prove that the fraction $\frac{24n+5}{18n+4}$ is in lowest terms. Is this solution going to be correct as a proof? Thanks for help!
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1answer
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Interesting Base summation contest math problem

The problem is as follows: Let $N_b=1_b+2_b+\cdots+100_b$ where $b$ is an integer greater than $2$. Compute the number of values of $b$ for which the sum of the squares of the digits of $N_b$ is at ...
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1answer
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Solving this equation

Question: Solve: $$3^{2x^2}-2\cdot3^{x^2+x+6}+3^{2(x+6)}=0$$ I thought that we can take $a=3^{x^2}$ and $b = 3^{x+6}$. Then equation becomes $a^2-2ab+b^2=0$, which obviously means $a-b=0$. ...