For questions about decimal expansion, both practical and theoretical.

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1answer
11 views

Cantor Set and Base 3 Decimal Expansions

I'm trying to show that every point in the Cantor Set (obtained by "middle-thirds" removal, starting with $[0,1]$) has a base 3 decimal expansion consisting of only zeros and twos. I think the proof ...
3
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2answers
56 views

Constructing A Space Filling Curve that fills the Unit Square

I'm reading Neal Carothers' Real Analysis, and he constructs a curve defined over $[0,1]$ that fills the unit square as follows: Let $f$ be a real-valued function over $[0,1]$ such that $f$ is $0$ ...
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0answers
23 views

Fixed decimal place sort problem [on hold]

I have a collection of randomly arranged fixed dp numbers, e.g. 5.0, 5.000, 5, 5.000000. The problem is to sort these numbers.
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1answer
18 views

Converting decimal dates to calendar dates?

I have the decimal number 2005.067 which represents the date January 25, 2005. The math equation below shows how the decimal number is created 2005 + (25 - 0.5)/365. I want to be able to grab 2005.067 ...
2
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2answers
19 views

How many numbers are in a numbering system with the basis 15 and 4 digits, where the digit sum equals 15

First of all, my question is very similiar to this one: How many numbers between $100$ and $900$ have sum of their digits equal to $15$? but i didn't quite understand how to adapt it to my problem, so ...
35
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1answer
511 views

Numbers $n$ such that the digit sums of $n, n^2,\cdots,n^k$ coincide.

Let $S(n)$ be the digit sum of $n\in\mathbb N$ in the decimal system. When I was playing with numbers, I noticed the followings : ...
0
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1answer
25 views

Multiplying numbers splitting the number into 4 digit numbers

Doing some programming exercise how to sum big numbers,I split the numbers into $n$ numbers of $4$-digit numbers $1240135981395813958$ I split into $1240$,$1359$,$8139$,$5813$,$958$ and summing with ...
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0answers
192 views

Numbers $n$ such that the digit sum of $n^2$ is a square

Let $S(n)$ be the digit sum of $n\in\mathbb N$ in the decimal system. About a month ago, a friend of mine taught me the followings : $$S\left(9\color{red}{^2}\right)=S(81)=8+1=3\color{red}{^2}$$ ...
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2answers
79 views

Prove: for all $n$ there's a $m$ such that the sum of digits in $mn$ is equal to $n$. [closed]

In the following $n,m$ are natural numbers. I need to prove that for all $n$ there's a $m$ such that the sum of digits in $mn$ is equal to $n$. Any ideas? Thanks.
25
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1answer
401 views

Does my “Prime Factor Look-and-Say” sequence always end?

I'm trying to create a challenge for PP&CG where the object will be to find the longest sequence in a given time, but I'm worried that there may be an infinite sequence that will ruin things. The ...
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4answers
142 views

How many digits are there in 100!? [closed]

How many digits are there in 100 factorial? How does one calculate the number of digits?
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0answers
24 views

Having problems understanding this algebraic expression

So I have a solution where $B = 0.1959552$ and $A = 0.00048515$. The problem asks, $A$ is $10$ times more likely than $B$. The teacher wrote (i.e. $A = 10 \cdot B$). Is this the right notation or ...
0
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1answer
40 views

$Pi(n) = Pi(n-2) + x\times [Pi(n-1)]$ for all convergent numerators and denominators. True?

Where $x = A001203$, $Pi = A002486$, $A002485$ $Pi(n) = Pi(n-2) + x\times [Pi(n-1)]$ for all $Pi > n+1 $ Hypothesis: This relation evaluates true for all $A002486$ and $A002485$. Lemma: All ...
1
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1answer
56 views

Given $x,y\in\mathbb R$ is there a “formulaic” way to obtain a $q\in\mathbb Q$ with $a<q<b?$

Is there an assignment of reals $x,y$ to a rational number $q(x,y)$ for which $$\forall_{\mathbb R} x.\forall_{\mathbb R}(x<y).\left(x<q(x,y)<y\right)\hspace{.2cm}?$$ For computable reals, ...
0
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1answer
24 views

How to round percents

Suppose there is election such that $n$ votes are given to $m$ candidates. I would like to express the results of elections in two decimal places, like ...
10
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1answer
123 views

Why do divisions like 1/98 and 1/998 give us numbers continuously being multiplied by two each time in decimal form?

For example, when I divided $1$ by $98$, I got an amazing result of $0.0102040816326530612244897...$ where so many numbers get multiplied by two every time in the right pattern with some carrying. ...
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5answers
2k views

How many even 3 digit numbers contain at least one 7.

How many even 3 digit numbers contain at least one 7. I got 126, but it was not an answer choice for the problem. Can anyone help?
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2answers
242 views

Real numbers as decimals

I'm looking for a book that develops the theory of real numbers in a rigorous way in terms of their decimal expansions. The exposition should be concrete and preferably aimed at mathematically ...
0
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2answers
107 views

Prepend a 9 or append a 0?

Given a positive integer $x$, will $x$ always be larger if one prepends a 9 in comparison to appending a 0? For x = 1, prepending is largest because $91 > 10$ For x = 9, prepending is largest ...
2
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1answer
44 views

Irrationality of Decimal Expansion of Primes

I've heard the proof that this number is irrational is accessible to even a novice to number theory: $\alpha = 0.2 \ 3 \ 5 \ 7 \ 11 \ 13 \ 17 \ldots$ The proof may utilize that a number is ...
0
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1answer
24 views

Decimal expansion__Represent numbers as $x = \sum_{k=1}^{\infty} \frac{a_k}{b^k}$?

If $b>1$ is an integer, is well know that the numbers $x\in (0,1]$, can be written as $$x = \sum_{k=1}^{\infty} \frac{a_k}{b^k}$$ for some integers $a_k \in \{0,1,\ldots ,b-1\} $. My problem is ...
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2answers
56 views
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9answers
3k views

Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?

Does $1.0000000000\cdots 1$ (with an infinite number of $0$ in it) exist?
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1answer
27 views

Does decimal fraction has hex value?/can hex be fraction?

I was wondering if a decimal fraction could be converted into a hexadecimal fraction? I have seen it many times ? but I have been also told that decimal or binary fraction has no meaning in hex. ...
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3answers
77 views

How would I find the decimal expansion of $1/99^2$

I want to find the repeating decimal expansion of $1/99^2$. All I know is that $1/99 = 0.010101\cdots$. How would I continue?
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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 ...
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1answer
60 views

The digit 3 and 2 digit number question

The digit 3 is written at the right of a certain 2-digit number forming a 3-digit number. The new number is 372 more than the original 2-digit number. What is the sum of the digits of the original ...
4
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1answer
75 views

Perfect squares formed by two perfect squares like $49$ and $169$.

Let $a$ be a perfect square number whose decimal representation is the concatenation of two perfect squares, for example $49$ (from $4$ and $9$), $169$ (from $16$ and $9$), ... and $4900$, $490000$ ...
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1answer
59 views

Usage of decimal expansion

I learned about the rigorous construction of rationals as a set of equivalence classes of ordered integers with operations defined on this set. I understand that the decimal expansion is another way ...
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4answers
121 views

Computing $0.0625^{-2.25}$ without a calculator

It is quite easy to see that $0.0625^{-2.25} = 512$ by plugging this into a calculator. Of course, mathematics existed for millennia before the invention of the calculator; is there a way to compute ...
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1answer
27 views

How to interpret fractional number of bits of precision

In double-precision floating-point format there're effective $53$ bits of mantissa stored. This lets us estimate maximum number of decimal digits of precision available: ...
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1answer
36 views

Numbers $n$ such that there is some digit occuring in each power of $n$

If a positive integer $n$ is congruent to $0$, $1$, $5$ or $6$ modulo $10$, there is some digit occuring in each of the powers of $n$. If the decimal expansion of $n$ ends in a $0$, $1$, $5$ or $6$ ...
4
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2answers
84 views

Find the 1005th digit after the decimal point expansion of the square root of N.

Let $N$ be the positive integer with $2008$ decimal digits, all of them $1$. That is, $N=1111...1111$, with $2008$ occurrences of the digit $1$. Find the $1005th$ digit after the decimal point ...
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2answers
128 views

Calculating decimal range for two's complement

Given this question : ...
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1answer
70 views

How to be unambiguous about a number's base's base?

Say you want to note down a number to another person, and want it to be unambiguous (perhaps the other person is an alien and has more than 10 fingers or something). So if you say 12345, base 42 ...
0
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1answer
55 views

Is there a 10-digit emirp?

Does a 10-digit emirp exist? Unfortunately, the lists of emirps I could find on the Web are quite small and my programming skills aren't good enough to write a program to check all the primes up to ...
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0answers
16 views

Lemma. $\exists N\in\mathbb{N}\forall n>N: x_n=0\Leftrightarrow x=\frac{q}{p^N}$ for some $q\in\mathbb{N}.$

https://proofwiki.org/wiki/User:J_D_Bowen/Math710_HW1 in the lemma of exercise 5 in direction $\Leftarrow$: Why $S_{N-1}=x$? I dont see! Thanks!
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4answers
50 views

Find all whole numbers such that the number increased by the sum of its digits equals 73.

I'm really lost on how to figure this out. Work shown would help.
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2answers
379 views

An arithmetic sequence whose members do not contain the digit ‘9’

There is a non-constant arithmetic progression made of natural numbers only; none of them contains the digit $9$. Prove that such an arithmetic progression has no more than $72$ terms.
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4answers
550 views

Numbers whose digits sum to 7

Let $S$ be the sequence of all positive integers whose decimal digits add to exactly 7, in increasing order: $$S = \langle7, 16, 25, \ldots, 70, 106, 115, 124, \ldots 160, 205, \ldots, 10230010, ...
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2answers
56 views

binary and floating point representation

suppose that we have following binary digits $00011001.110 $,we can do following thing $00011001.110=1\cdot2^4+1\cdot2^3+1\cdot2^0+1\cdot2^{-1}+1\cdot2^{-2}=25.75$ then what does means? We then ...
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4answers
728 views

Are there numbers that describe themselves in some base but not according to the pattern 6210001000?

Call the first digit of a number digit 0. The digit after that digit 1, and so on and so forth. In base 10, the number 6210001000 describes itself, because digit 0 is 6 and it has 6 0s. Digit 1 is 2 ...
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2answers
54 views

Decimal expansion of a fraction [duplicate]

I was reading something which I found really special. It goes like this : Imagine we have a line with unity division (0,1,2,etc.) Now, we have a point on this line. The point can be on a point of ...
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2answers
545 views

How many digits are there in $2^{17}\times 3^2\times 5^{14}\times 7 ?$

How many digits are there in $$2^{17}\times 3^2\times 5^{14}\times 7 ?$$ Question added: I agree with the fellow who asked that if one cannot have 2 and 5 in the number above how we will calculate ...
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0answers
27 views

Non-repeating decimals in 1/n [duplicate]

Here's a conjecture I made: The number of non repeating decimal places in the base-ten representation of the fraction 1/n, where n is an integer, is equal to whichever is higher: the exponent of 2 in ...
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2answers
182 views

A question about decimal representation of irrational numbers.

Is this true that any finite word of the alphabet $\mathcal{A_9}=\{0,1,2, \ldots,8,9\}$ appears somewhere in the decimal representation of $\sqrt{2}$ ? Thanks !
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2answers
254 views

Compute and find 2009th decimal(2009th digit after the point), without automation, the following sum

Compute and find 2009th decimal of (2009th digit after the point), without automation, the following sum $$\frac{10}{11}+\frac{10^2}{1221}+\frac{10^3}{123321}+ \cdots ...
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1answer
86 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 ...
5
votes
1answer
156 views

patterns in the decimal expansions of adjacent square and cube roots

For fun I made a table in Excel which evaluated the square and cube roots of whole numbers in ascending order. Then of the result, I extracted the first, second and third decimal place digits, then ...
3
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2answers
64 views

Cannot find length of repeating block in decimal expansion for $\frac{17}{78}$

I am trying to find the length of of the repeating block of digits in the decimal expansion of $\frac{17}{78}$. On similar problems, that has not been an issue. Take for instance $\frac{17}{380}$. My ...