The decimal-expansion tag has no wiki summary.
2
votes
1answer
34 views
What is the terminology for the non-repeating portion of a rational decimal?
Given a number co-prime with 10, such as thirteen, we can construct a repeating decimal from its reciprocal: $\frac{1}{13}$ = 0.(076923). If we successively divide this number by a factor of 10 (i.e., ...
8
votes
2answers
82 views
Irrational numbers, decimal representation
Can this even be proved? (Or disproved?)
Any irrational number without a 0 (zero) in its decimal representation is transcendental.
Not sure where to start on this one...
0
votes
0answers
19 views
Analysis and n-adic expansions
I am trying to discern some mathematical term known as a $n$-adic expansion. For example the book I am reading says: write every $x \in[0, 1]$ its "$4$-adic" expansion
\begin{equation}
x = ...
0
votes
1answer
25 views
Uniqueness of nonterminating decimal expansion…
Prove that decimal representation is unique iff the number has no terminating expansion. Prove also that any terminating expansion also has a nonterminating expansion. How are these nonterminating ...
1
vote
1answer
25 views
XOR for 10 and 20
I know that this is the XOR truth table.
A B Q
------
0 0 0
0 1 1
1 0 1
1 1 0
I have a = 10; and b=20; Their respective binaries are a=1010; and b=10100;
a ...
9
votes
7answers
1k views
Is 1 divided by 3 equal to 0.333…?
I have been taught that $\frac{1}{3}$ is 0.333.... However, I believe that this is not true, as 1/3 cannot actually be represented in base ten; even if you had ...
1
vote
1answer
26 views
Convergence of an infinite product of a quotient of an irrational number and its decimal expansion
I did some exploring with Mathematica about infinite products of quotients of limits of sums and their quotients with increasing partial sums. I didn't discover much, but I would like to ask the ...
3
votes
1answer
129 views
Period of repeating decimals
Note: This question is base sensitive. Therefore, assume we have fixed a base $b$. By abuse of terminology, I will still use the word "decimal".
This question revolves around the period of repeating ...
3
votes
1answer
53 views
Characterization of non-unique decimal expansions
In proofs exhibiting bijections of $\mathbb{R}$ for the sake of proving arguments about cardinality, care is generally taken to avoid the $.999\!\ldots=1.00\!\ldots$ problem. However, it is generally ...
1
vote
1answer
50 views
Explicit Fractional Basis Expansion
We can write any $x\in\mathbb R$ as its $b>1\in \mathbb N$ basis expansion:
$$x=sgn(x)\sum_{d=-\infty}^\infty b^d \lfloor |x|b^{-d} - b\lfloor |x|b^{-d-1} \rfloor \rfloor$$
Can one come with the ...
2
votes
1answer
57 views
Is there a sequence of primes whose decimal representations are initial segments of each other?
I.e., is there a sequence of primes whose decimal expansions have the following form:
$$a_1,\ a_1a_2,\ a_1a_2a_3,\ a_1a_2a_3a_4, \dots$$
What about with the order of the digits reversed, so each ...
1
vote
1answer
187 views
Find $N$, in the decimal expansion of the large number $N=4^{4^{4^4}}$
Find $N$, in the decimal expansion of the large number
$$N=4^{4^{4^4}}$$
Following on from the question I posted yesterday about finding the number of digits
( Find the number of digits, $D$, in ...
11
votes
1answer
138 views
Square root of an integer has only even digits
Is there a non-square positive integer $n$, that $\sqrt{n}$ has only even digits in its decimal representation ?
1
vote
1answer
22 views
Calculating the yearly interest?
i am doing a task where i met the following problem:
How can I calculate the yearly interest, with at least three decimals, when the monthly interest is 3.4%?
For me it seems hard to figure out a ...
0
votes
2answers
75 views
floating point binary arithmetic
Prove that the decimal number $\displaystyle \frac{1}{5}$ cannot be represented by a finite expansion in the binary system.
1
vote
2answers
76 views
Finite representation in the binary $\implies$ finite representation in the decimal system
Any number that has a finite representation in the binary system have a finite representation in the decimal system. Why?
2
votes
0answers
30 views
Basic arithmetic operations formalized with decimal expansions
Suppose I have two real numbers $a$ and $b$ with decimal expansions
$a = \sum_{i=0}^{N_a} a_i 10^i + \sum_{i=1}^\infty a_{-i} 10^{-i}$ and $b = \sum_{i=0}^{N_b} b_i 10^i + \sum_{i=1}^\infty b_{-i} ...
7
votes
1answer
486 views
Why decimal expansion of $e$ has two copies of $1828$
Is there any explanation why the block $1828$ occurs twice in the decimal expansion of the transcendental $e$, $2.718281828459\ldots$, but is not recurring?
0
votes
6answers
104 views
How to multiply decimal with wholenumber?
How Can I multiply
x = (0.35)(80)
x = 28
steps by step fastest way
I am not going to lie, but it is time for me to take a test without using a calculator.
Schools have made me worse by giving us a ...
1
vote
1answer
357 views
Signed 10's complement
I know what is 10's complement of a number, but what is signed 10's complement? I could not find an explanation about it. How can one do addition using signed 10's complement?
0
votes
1answer
74 views
Decimal expanson of the reals
I came across a problem I would like to ask you about:
Let $x$ be a real number. Iwant to show that $\exists b \in Z$ and integers $ b_1, b_2,b_3, \ldots\in \left\{{0,1,\ldots,9}\right\}$ so that the ...
4
votes
1answer
174 views
What is the representation for a number that is not quite one?
If: $$0.\overline{9999999} \equiv 1$$
Then how would you represent a value that is infinitesimally close to one, but not quite one?
i would have thought: $$1-\frac 1 \infty $$
But i would take that ...
3
votes
1answer
121 views
Convention of digit grouping after decimal point
I read that different cultures have different ways of grouping digits before the decimal point for readability e.g. 1234567890 can be grouped as 1 234 567 890 (English), 12 3456 7890 (Chinese) or 1 23 ...
1
vote
0answers
56 views
Effect on decimal values rounded to the nearest binary representable power of ten precision?
Actually i have some property in my chart control which create auto scale and enable setting that decimal values should be rounded to the nearest binary representable power of ten precision.
If i ...
1
vote
0answers
125 views
Change fraction to decimal
Can anyone please help.
I'm following a tutorial found here as I have a situation where I have to get the equation of a line in point slope form i.e. $y - y_1 = m(x - x_1)$
I get up to step 3 of the ...
0
votes
1answer
165 views
Can the BBP formula be used to prove that Pi is normal?
Can the BBP formula be used to prove that Pi is normal?
http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula
http://en.wikipedia.org/wiki/Normal_number
13
votes
6answers
572 views
Calculate the 146th digit after the decimal point of $ \frac{1}{293} $
The question is: Calculate the 146th digit after the decimal point of $\frac{1}{293}$
1 / 293 = 0,00341296928.., so e.g., the fifth digit is a 1.
We know that 293 is a prime, probably this would ...
57
votes
4answers
5k views
What is special about the numbers 9801, 998001, 99980001 ..?
Just saw this post, and realized that
1/9801 =
...
0
votes
2answers
559 views
How do I evalulate a fraction (example 1/998001) accurately to 100 decimal places and then display it in maxima/wxmaxima??
I am trying to evaluate a decimal expansion of a fractional value to a large number of digits of precision (in this example 100):
...
0
votes
2answers
2k views
Do the digits of $\pi$ contain every possible finite-length digit sequence? [duplicate]
Possible Duplicate:
Prove there are no hidden messages in Pi
This is not a practical problem. I am asking out of curiosity. Any links/references are most welcome.
Say, we write the digits ...
11
votes
1answer
606 views
Interesting pattern in the decimal expansion of $\frac1{243}$
There appears to be an interesting pattern in the decimal expansion of $\dfrac1{243}$:
$$\frac1{243}=0.\overline{004115226337448559670781893}$$
I was wondering if anyone could clarify how this ...
1
vote
2answers
174 views
Upper and lower bounds in regards to 0.(9) [duplicate]
Possible Duplicate:
Does .99999… = 1?
I'm only doing this at GSCE and I'm really only asking here because of an interesting email conversation between my Grandfather and I regarding ...
4
votes
3answers
291 views
The number of ones in a binary representation of an integer
Is there any relation that tells whether the number of ones in a binary representation of an integer is an even or an odd number?
4
votes
4answers
494 views
Are there any other numbers like $0.999\ldots$?
In a manner similar to how the value $1$ can be represented as $0.(9)$ too, are there any other values that exhibit this property when represented in base 10?
9
votes
3answers
607 views
Cyclic numbers are characterized by the reciprocals of full reptend primes?
The number $142,857$ is widely known as a cyclic number, meaning consecutive multiples are cyclic permutations, i.e.
$1 × 142,857 = 142,857$
$2 × 142,857 = 285,714$
$3 × 142,857 = ...
1
vote
1answer
91 views
How does x+y = x for non-zero value of y in floating-point arithmetic?
So, as the question asks, is we have only normalised floating-point values and normalised results, could you please explain how x + y = x?
I know it all relates to precision, but how can I explain ...
0
votes
1answer
215 views
I'm puzzled with 0.99999 [duplicate]
Possible Duplicate:
Does .99999… = 1?
After reading all the kind answers for this previous question question of mine,
I wonder... How do we get a fraction whose decimal expansion is ...
2
votes
4answers
272 views
How do we find a fraction with whose decimal expansion has a given repeating pattern?
We know $\frac{1}{81}$ gives us $0.\overline{0123456790}$
How do we create a recurrent decimal with the property of repeating:
$0.\overline{0123456789}$
a) Is there a method to construct such ...
2
votes
1answer
242 views
Upper bound/exact length of decimal expansion of simple fraction
E.g. 1/8=0.125 has three decimals when written out in base 10, but what is a good example of a simple fraction where the decimal sequence terminates but is very large?
Is there some sort of rule ...
7
votes
3answers
2k views
Prove there are no hidden messages in Pi
Assume that a proof that pi is normal existed.
Is it then possible that starting at some finite position x in pi, from there on every p(n)'th digit is 0, where p(n) is the n'th prime?
I know ...
12
votes
2answers
433 views
Have all numbers with “sufficiently many zeros” been proven transcendental?
Any number less than 1 can be expressed in base g as $\sum _{k=1}^\infty {\frac {D_k}{g^k}}$, where $D_k$ is the value of the $k^{th}$ digit. If we were interested in only the non-zero digits of this ...
5
votes
1answer
706 views
On the binary decimal expansion of the reciprocal prime's
I have been thinking a little bit about the binary decimal expansion of reciprocal prime numbers; and I have a few questions.
I found this neat table which lists the binary expansion of many ...
13
votes
2answers
823 views
Why is the decimal representation of 1/7 “cyclical”?
1/7 = 0.(142857)...
with the digits in the parentheses repeating.
I understand that the reason it's a repeating fraction is because 7 and 10 are coprime. But this...cyclical nature is something ...
12
votes
19answers
7k views
Does .99999… = 1?
I'm told by smart people that 0.999... = 1 and I believe them but is there a proof that explains why?
