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4
votes
3answers
472 views

Dividing Decimals.. But remainders?

So, I understand how to do long division with decimals. So let's consider this problem: $10.5$ divided by $5.5$ (I chose this problem because it will OBVIOUSLY have a remainder) So we will look at ...
1
vote
1answer
193 views

How to calculate decimals of the fractional number 1/49?

I find this tricky one. How to calculate the first 50 digits/decimals of the fractional number 1/49? Two of my calculators and MatLab gives different answers so I'm curious, how this is calculated ...
4
votes
1answer
79 views

First digits of extremely large binomial coefficients

Can the first digits of a binomial coeffecient $$\binom{n}{k}$$ be calculated, if n and k are very large numbers ? For example Calculate the first ten digits of $$\binom{10^{85}}{10^{23}}$$ Any ...
2
votes
0answers
78 views

First digits of extremely large numbers (Generalization of “first digits of Graham's number”)

I found a question about the first digits of Graham's number and would like to generalize it : We want the first n digits of the number $a\uparrow^b c$. Which method is the most effective to do ...
8
votes
0answers
93 views

Biggest powers NOT containing all digits.

Let $m>1$ be a natural number with $m \not\equiv 0 \pmod{10}$ Consider the powers $m^n$ , for which there is at least one digit not occurring in the decimal representation. Is there a largest $n$ ...
5
votes
3answers
222 views

What is the smallest natural number n?

What is the smallest natural number n for which there is a natural k, such that, the lasts 2012 digit in the representation decimal of $n^k$ are equal to 1? I don't even know how to start with it ... ...
2
votes
2answers
85 views

Which real numbers have two representations?

Are they only numbers that end with 9999... and 0000... after the dot or some other too? If so, can you give an example?
0
votes
2answers
78 views

Decimal expansion of a Cauchy sequence

In one of the construction of $\mathbb{R}$ we make each real number an equivalence class of Cauchy sequences in $\mathbb{Q}$. More precisely, two Cauchy sequences $a_n$ and $b_n$ are equivalent iff ...
1
vote
0answers
76 views

Why are normal numbers important?

I'm studying normal numbers for my university dissertation - in particular whether or not algebraic numbers are normal. One thing I cannot find anywhere is why it matters. I'm not expecting a real ...
10
votes
3answers
305 views

Is a decimal with a predictable pattern a rational number?

I'm starting as a private Math tutor for a high school kid; in one of his Math Laboratories (that came with an answer sheet) I was stumped by an answer I encountered in the True or False section (I'm ...
2
votes
0answers
38 views

A four-digit square is of the form $aabb$. What's $a^2+b^2$? [duplicate]

The 5772 Ulpaniada included the following question: Consider a four digit square number (a number which is the square of a whole number).Its digit notation is $aabb$ (the thousands digit is $a$, ...
0
votes
3answers
153 views

Why does $0,\bar{9}$ equal $1$? [duplicate]

I am finding hard to understand why $0,99999..... = 1$ I have the following proof: Let $x$ be $0,9999...$ then $10x = 9,999...$ So $10x - x = 9,999 - 0,9999$ $9x = 9 \rightarrow x = 1$ From a ...
1
vote
4answers
54 views

How do I convert from binary base to decimal?

I have a homework problem and I don't understand it. Here is the problem: The base two number 11111(base 2) has the same digit in all places. The same number can be written in different bases. Find ...
2
votes
1answer
68 views

Calculating 6 decimal digits of $3^{\sqrt2}$ using a calculator.

How can we calculate $3^{\sqrt2}$ to 6 decimal digits, using only a semi-basic calculator (Which has the square root too) and a pen and paper? I asked this question from my teacher and he ...
0
votes
0answers
27 views

How to convert decimal number to base -10 [duplicate]

How to convert from decimal (base 10) number to base -10? For example, $$ -44 \mapsto 56_{-10}, $$
1
vote
2answers
266 views

converting decimals to base negative-10

I have a decimal (base $10$) number, $44$, and would like to convert it to base $-10$. I know how to convert $$ 164_{-10} \mapsto 44_{10}, $$ but not the other way around.
2
votes
1answer
80 views

Fractions and long division. [duplicate]

$\frac{1}{9}=0.111\dots$ $9\times \frac{1}{9} = 0.999\dots$ $1=0.999\dots$ What is the problem here? Thanks for any help.
4
votes
0answers
85 views

Arrow notation and decimals.

We know how to add with decimals. We know how to multiply with decimals. We know how to exponentiate with decimals. Do we know how to work with decimals for power towers? for example, can we deal ...
1
vote
2answers
46 views

Divisibility by $9$

Suppose we have a natural number $N$ with decimal representation $A_kA_{k-1}\ldots A_0$. How do I prove that if the $\sum\limits_{i=0}^kA_i$ is divisible by $9$ then $N$ is divisible by $9$ too?
3
votes
0answers
62 views

Decimal system history

Today, "numbers" usually refer to real numbers and are most commonly conceptualized as consisting of all possible infinite decimal expansions (or binary expansions, etc). When did this way of thinking ...
2
votes
2answers
35 views

How to identify whether a fractional part of a number contains more that 2 digits.

EX. I want to accept numbers which have maximum of 2 digits after decimal points. i, e, 10.23 should be allowed and 10.233 should not be allowed. What mathematical operations can be done to ...
1
vote
1answer
138 views

About the sum of the first half and the latter half of the cyclic numbers of a repeating decimal

Let us call the sum of the first half and the latter half of the cyclic numbers of an irreducible fraction 'a division sum' when the period of a repeating decimal is even. Also, let $\lambda(l)$ be ...
21
votes
2answers
500 views

$\lfloor0.999\dots\rfloor= ?$ $0$ or $1$?

I think $\lfloor0.999\dots\rfloor= 1$, as $0.999\dots=1$,but I have doubt, as $\lfloor0.9\rfloor=0$,$\lfloor0.99\rfloor=0$,$\lfloor0.9999999\rfloor=0$, etc.
3
votes
1answer
86 views

Which Well-Known Numbers Are Alexandrian

A real number is said to be Decimal Alexandrian if its decimal representation contains every possible finite decimal sequence. It is a popular question whether $\pi$ is Decimal Alexandrian, or even in ...
1
vote
0answers
64 views

Prove that x has two base p decimal expansions

I am attempting to prove that if $x$ has a finite-length base $p$ decimal expansion, that it has precisely two base $p$ expansions. ($x = \frac{a_1}{p} + \dots +\frac{a_n}{p^n}$) My attempt: x can ...
2
votes
1answer
43 views

Cont'd Decimal Expansion, rational or not?

This is a follow up from this question. Since it's proven by Calvin Lin that $0.11235813213455...$ (Fibonacci Sequence), I'm not wondering if the sequence $$0.123456789101112131415...$$ (which is ...
0
votes
1answer
39 views

Representing a strange number as a fraction

Can this decimal with special patterns be expressed as a fraction? Is it a rational number? $$0.101001000100001000001...$$ Where the number of zeros after every 1 is increased by 1. Ty.
16
votes
2answers
642 views

Is the number $0.112358132134…$ rational or irrational?

Just out of curiosity, is the number $0.112358132134...$ a rational or irrational number? $...$ stands for Fibonacci sequence not repeating decimals!
0
votes
3answers
240 views

Is $0.9999…$ an integer? [duplicate]

Just out of curiosity, since $$\sum_{i>0}\frac{9\times10^{i-1}}{10^i}, \quad\text{ or }\quad 0.999\ldots=1,$$ Does that mean $0.999\ldots=1$, or in other words, that $0.999\ldots$ is an integer, ...
1
vote
2answers
105 views

CS problem, turned to mathematics

I am trying to solve some of the projecteuler problems using a much of a programmers approach. However, I would like to get more into the math, and therefore would try to do some mathematical ...
1
vote
3answers
86 views

Are there axioms or theorems about the decimal terminations of numbers?

I've got struck by curiosity: Are there axioms or theorems about the decimal termination of numbers? For example: $$\frac{1}{3}=0.3333333333333333\ldots$$ And ...
0
votes
3answers
125 views

Is this statement true: 1 = 0.99 [duplicate]

Now this question might sound a bit weird to some people, but the situation is this: Say I have the number $0.999..$ where there is an infinite number of 9's (much like $0.3333..$ with ...
1
vote
1answer
223 views

Period of a decimal expansion

Show that if n is a product of m distinct primes, then the period of the decimal expansion of 1/n is the lowest common multiple of the periods of 1/p over all primes p|n. I understand that the above ...
1
vote
1answer
77 views

Problem using decimal expansion of a number

Please give me some information about decimal expansion of numbers so that I could try out this problem.
3
votes
1answer
96 views

The number of zeros in the decimal representation of the factorial of 126

How many zeros are in $126!$ ... the result is $34$. But can I calculate it manually? I have seen How many zeroes are in 100! but I don't think it's helpful.
0
votes
1answer
26 views

How to find proportions: x as a proportion of y.

I have two questions, firstly, what is 21 as a proportion of 510 (expressed as a decimal), and secondly, what is 66 as a proportion of 510 (expressed as a decimal)?
9
votes
2answers
367 views

The $2013$th digit of $1234567891011213141516\ldots$

How do I find the $2013$th digit of the number $12345678910111213141516\ldots$ I still don't get it, how are you suppose to find the exact digit. How did you hint help at all?
6
votes
1answer
159 views

Are there any real (especially irrational) numbers whose decimal expansion and continued fraction are the same?

If a number with more than one digit occurs in the fraction, it should be expanded to as many digits in the expansion. I will be even more impressed, however, if the fraction consists entirely of ...
10
votes
1answer
285 views

How many zeroes are there at the end of the sum $1^1 + 2^2 + 3^3 + \cdots+ 100^{100}$?

Find the number of zeroes at the end of the sum $$1^1 + 2^2 + 3^3 + \cdots+ 100^{100}$$ I tried a lot and my answer came 4700 but it was not correct.
0
votes
1answer
90 views

what is the new order of the digits here ? Both the numbers $144$ and $441$ consists of the same digits?

$12^2=144$ Here in, $144$ the hundreds digit is 1. The $1$ has travelled to the units place below in $21$ as well as $441$. $21^2=441$ What can be said of the $4's$ ?
3
votes
1answer
238 views

IBM Research Ponder This (June Challenge)

This was the challenge in last month's 'IBM Reseach Ponder This'. I just cannot get my head around the solution posted. Can someone explain further? Challenge Find a rational number (a fraction of ...
0
votes
2answers
79 views

How many of the 0 digits are place holders in 330.606?

How many of the 0 digits are place holders in 330.606? This is the problem. I have tried solving it on the online calculator.
25
votes
13answers
4k views

Is it possible to have multiple decimal points in a number?

Is it ever possible to have multiple decimal points in a number? If so, how? For example is the value 1.1.2 possible? This is a question posed purely out of curiosity.
0
votes
2answers
57 views

Find digits $x$, $y$, $z$, and $p$ such that $(xyzp)_{10}=4\cdot (pzyx)_{10}$

Given that equation $xyzp=4\cdot pzyx$ is valid, how do I solve showing my work clearly? By trial and error the valid answers are $x=8,y=7,z=1,p=2$. These are the only conditions provided.
4
votes
1answer
138 views

Length of recurrent strings of numbers in the decimal expansion of $1/p$, where $p$ is prime.

Am I right to assume that: all rational numbers have a recurrent sequence in their decimal expansion, and the length of the expansion of $1/p$, where $p$ is prime, is $p-1$ for sufficiently large ...
4
votes
1answer
147 views

Is every day tau day (or pi day) to some base?

People on my facebook wall are celebrating the fact that today is tau (2 pi) day—6/28. This got me thinking: today is only tau day because we represent numbers in decimal base. Could every day of the ...
1
vote
1answer
815 views

Converting decimal ratio to a percentage

Note before; I have searched the site and can't find an answer to this question, so that I wouldn't make a duplicate. I couldn't find the answer already so I either didn't search properly, or this ...
3
votes
0answers
98 views

Decimal representation and Peano axioms

I really tried to find similar questions but didn't manage to find them. Please, forgive me if this question is a duplicate. I also apologize for my English. So. The question. We're given five Peano ...
5
votes
2answers
288 views

How many ways are there to represent the number $N$?

I was given a task that doesn't require any special knowledge of math, but got stuck with it. Here it is: How many ways are there to represent the number $N$ in the following way: $$ N = a_3 \cdot ...
0
votes
2answers
90 views

Definition of period of a decimal representation of a number

I need to define the period of a decimal representation of a number!! Thanks in advance!!