The tag has no wiki summary.

learn more… | top users | synonyms (1)

1
vote
3answers
66 views

How to round $ 0.03446$ to three decimal places?

What is $ 0.03446 $ rounded to three decimal places? I think it is $0.035$ but someone told me that it should be $0.034$. I think $0.035$ because the $6$ would change the $4$ into a $5$, which ...
2
votes
1answer
62 views

What Will Happen Without Decimal Expansion?

After a discussion on the complexity of decimal expansion (such as $0.\bar{9}=1$), some of my students (middle school) decided to throw away the decimal expansion of some numbers! Namely, the numbers ...
3
votes
1answer
186 views

$\displaystyle \frac{6}{2n-1} - \frac{1}{n} = \frac{p}{2^i5^j}$

$\displaystyle \frac{6}{2n-1} - \frac{1}{n} = \frac{p}{2^i5^j}$ For which $n$ is this expression true. $n$ and $p$ are integers. $i$ and $j$ are positive integers or zero.
4
votes
3answers
50 views

Graph of the last digit of $x^n$ - why is it symmetric when $n$ is even, and not when $n$ is odd?

I have discovered this fact: "The graph of the last digit of $x^n$ (where $x$ is positive) is asymmetrical if $n$ is odd, and symmetrical if $n$ is even." What is the logic behind this? For ...
0
votes
1answer
44 views

Finding number of primes of the form $1010\ldots 101$ (in base 10) [closed]

How many primes among the positive integers, written as usual in the base $10$, are such that their digits are alternating $1$’s and $0$’s, beginning and ending with $1$?
0
votes
3answers
53 views

How to do long division $1.068 / 40$ without using a calculator?

1.068 divided by 40. 1.068 / 40 = ? How would you do this problem by long division and any other methods to figure this out without using a calculator. Just pencil and paper.
-1
votes
2answers
38 views

11th form to 7th form

I can't solve this one: Consider an integer expressed in the 11-based form. In the 11-based form, digits 0 to 9 correspond to their decimal values, and A corresponds to 10. For example (15)_11 = (1 * ...
1
vote
1answer
116 views

What are the last 20 digits of mega?

What are the last 20 digts of the number mega, which is "2 in a pentagon" in steinhaus-moser-notation ? In contrary to power towers or tetration, the ending digits are not stable. I found out that ...
7
votes
0answers
83 views

Which digit occurs most often?

Is there any method to calculate, which digit occurs most often in the number $$4 \uparrow \uparrow \uparrow \uparrow 4\ ,$$ the fourth Ackermann-number ? Or would it be necessary to calculate the ...
0
votes
1answer
91 views

do you know another Magic Square with this property?

with the repeating digits of $\frac{1}{19} = 0.052631578947368421$ we can construct an exceptional magic square : The number 19 is a cyclic number with a period of 18 before the digits start to ...
4
votes
3answers
474 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
278 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
85 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
1answer
106 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
96 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
253 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
98 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
123 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
78 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
443 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
159 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
55 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 ...
1
vote
2answers
297 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
81 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
92 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
64 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
39 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
149 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 ...
20
votes
2answers
512 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
90 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
72 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
45 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
40 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
677 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
254 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
108 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
88 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
131 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
240 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
82 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
104 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
27 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
291 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 $4's$ ?
4
votes
1answer
254 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 ...