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.

learn more… | top users | synonyms (1)

6
votes
1answer
423 views

What is the Scientific Notation of Zero?

This question was asked here, where the answer uses this description. The last line reads: "The special case of $0$ does not have a unique representation in scientific notation, i.e., ...
3
votes
1answer
39 views

Let x and y be two positive real numbers with x<y. Using only the axioms for real numbers, show that 0 < 1/y < 1/x

Let x and y be two positive real numbers with x < y. Using only the axioms for real numbers, show that 0 < 1/y < 1/x I apologize for how it looks, but I'm not very good with formatting. How ...
0
votes
2answers
28 views

The perfect Number system

I was thinking of the number system presently in use(the decimal system) and its shortcomings. One of them is that all numbers cannot be represented accurately, for example the value of any irrational ...
3
votes
2answers
29 views

Even integer in ternary representation

Suppose $(d_0,d_1...d_k)_3$ is the ternary representation of a even integer $n$. Show that there is an even number values $d_0...d_k$ that are odd, whenever $n$ is even. I have tried decomposing ...
0
votes
1answer
46 views

Does anyone knows about Ethiopian numerals?

I'm wondered if anyone could give me best resource about Ethiopian(Geez) Numerals and Could you write Geez on LaTex? Thank you very much!
1
vote
3answers
47 views

Convert 2620.123 base 10 to base 5

I understand the integer part, keep dividing by 5 and I get 40440, but for the fraction part I did a calculation, but it does not match with the answer given. I do the fraction part like this: ...
4
votes
3answers
96 views

subtraction of two repeating decimals rationals

When I was looking at the proof that every repeating decimal is rational, I came across this example: $x=5.33333333\ldots$ ($3$ repeat indefinitely) $10x=53.3333333\ldots$ ($3$ repeat indefinitely) ...
0
votes
2answers
69 views

Why non-real means only the square root of negative?

Once in 1150 AD, an Indian mathematician Bhaskara wrote in his work Bijaganita (algebra) that, There is no square root of a negative quantity, for it is not a square However later on in 1545 an ...
0
votes
2answers
55 views
0
votes
0answers
15 views

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). ...
0
votes
0answers
11 views

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 ...
0
votes
1answer
52 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 ...
4
votes
1answer
52 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 ...
4
votes
1answer
71 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 ...
0
votes
2answers
52 views

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 ...
1
vote
1answer
82 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". ...
0
votes
1answer
27 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 ...
3
votes
0answers
31 views

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 ...
1
vote
1answer
24 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 ...
0
votes
1answer
30 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 ...
0
votes
0answers
32 views

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?
51
votes
10answers
6k views

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 ...
1
vote
1answer
44 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: $(3a+5 + 2a+4) * (2a+1) = 108a + 1$ ...
1
vote
0answers
29 views

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: ...
0
votes
1answer
46 views

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? ...
1
vote
2answers
32 views

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? ...
3
votes
1answer
41 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 ...
0
votes
0answers
17 views

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 ...
0
votes
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 ...
1
vote
1answer
54 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 ...
-4
votes
1answer
56 views

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 ...
3
votes
0answers
47 views

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 ...
0
votes
0answers
55 views

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 ...
2
votes
1answer
75 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 ...
1
vote
2answers
33 views

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.
1
vote
4answers
100 views

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 ...
1
vote
1answer
28 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.
-1
votes
1answer
39 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?
0
votes
0answers
33 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 ...
2
votes
1answer
84 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 ...
0
votes
1answer
69 views

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 ...
6
votes
4answers
131 views

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 ...
0
votes
2answers
1k 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 ...
-2
votes
1answer
52 views

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 ...
4
votes
1answer
346 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 ...
1
vote
1answer
40 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} + ...
0
votes
1answer
47 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: ...
0
votes
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 $(n+1)^+=n+1+1=n^++1$
0
votes
2answers
72 views

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 ...
3
votes
3answers
292 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?