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Questions tagged [scientific-notation]

A way of expressing numbers in the form $a \cdot 10^b$, where $a$ is a real number and $1 < a < 10$, and $b$ is an integer, otherwise known as standard form. This is a concise way to express very large or very small numbers.

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How to properly note a subset which contains overlapping sets

I try to describe the logic of some algorithms I perform on meshes (in finite element analysis). suppose i have some elements called e within some domain $E_\Omega$, each being a set of nodes n. Those ...
Daniel's user avatar
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$10^6 = 1000000$, which has $6$ zeros before decimal. Then why does $10^{-6} = 0.000001$, has only $5$ zeros after decimal?

I just can't get my head around this. Now I know that $10^{-n}$ = $\frac{1}{10^n}$. But I just can't understand the logic. My question may sound stupid to most people here but I am a beginner at math ...
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notation for clusters of 2D data points

Is there any convention about the notation to use for clusters of $2-$D data points? I have a set of clusters of $2-$D data point. I can denote each cluster with $c_i$, where $i = 1, 2, ..., n$, and $...
Ommo's user avatar
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Notation about the size of a subset

Introduction. I have three indices, $i$, $j$ and $l$ indicating, respectively, the $i^{th}-$element, the $j^{th}-$element and the the $l^{th}-$element of a set of 2-dimensional points $P=\{ p_1, p_2, ...
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Conventions on subscripts and superscripts: "Math mode" or "text mode" for (relatively long) words?

Is there any mathematical convention on the mode of writing (relatively long) words in subscripts or superscripts, i.e. either with a Latex math mode or with a text mode? For example: math mode: $A^{...
Ommo's user avatar
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Round the following number to $4$ significant figures: $794834.$

Round the following number to $4$ significant figures: $X=794834.$ For the number $X=794834$, I simply observed that all the digits in here are significant. The $4^{th}$ significant digit in this case,...
Thomas Finley's user avatar
3 votes
2 answers
313 views

Is it possible to determine how many digits are required to represent an equation?

Maths isn't my strong point, so bear with me... Consider the following equation: 65536 ^ -23 Scientific Notation 1....
Matthew Layton's user avatar
1 vote
1 answer
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Notation question $\vee$ in a probability proof

I'm working on probability, more precisely on Brownian motions and I'm following a book by Peter Mörters and Yuval Peres and they used the following notation ($\vee$): $$\left\{\exists t\in[0,1): \...
PNM's user avatar
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2 votes
1 answer
59 views

Notation of recursive function with multiple arguments

I want to formally describe an algorithm $f : E \times P \to P$ which you can use as an argument for itself. Right now, I have the following definition: \begin{equation} \begin{split} P_{e_{n+1}} &...
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Are there any ways to increase the precision in MATLAB without built in functions?

I am a beginner learning about MATLAB scientific computation, floating point numbers, and numerical error. When I am using a very small $x$ value for some equations, such as $y(x) = (\exp(x)-1-x)/x^2$,...
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3 votes
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Explanation for MATLAB floating point number calculation?

I am a beginner studying scientific computation, more specifically floating point numbers and precision in matlab. When testing the outputs of 2 of the following equations, I am not sure how matlab ...
cronk's user avatar
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5 votes
3 answers
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How to denote an ordered list, indicating that the order is not known beforehand

I have a set of states $A = ${$ a_0, a_1, ..., a_n $}. A model predicts $y$, an ordered list in which these states were observed over time, e.g. $y = (a_3, a_1, a_4)$. Not every $a_i$ in $A$ needs to ...
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Inconsistent math in multiplication or Python's multiplication implementation is at fault?

Is it wrong to say every number in mathematics is simply a fractional number, and any operation performed on them would always return the same output ? If not, then please explain why the following <...
GypsyCosmonaut's user avatar
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Short hand notation for long chains of functional compositions

I understand from an earlier Math SE query: https://math.stackexchange.com/q/2719645 the following short hand notation could be used to express long chains of functional compositions (?) : $f(x)=\...
Zebra Fish's user avatar
-1 votes
1 answer
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What's the difference between $|\overrightarrow{v}|$ and $\|\overrightarrow{v}\|$ [closed]

What's the difference between these two signes $|\overrightarrow{v}|$ and $\|\overrightarrow{v}\|$ for a given vector $\overrightarrow{v}$?
Artashes's user avatar
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Is there such a thing as a scalar absolute field?

I have a mathematical expression which I feel must be a better / more formal representation. The best way I can think to describe it is as a "scalar absolute field" (but there maybe a better ...
Suzie Q.'s user avatar
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27 views

Is there any notation for a set of real valued bounded functions and the notation also include the information of bounds?

For, e.g., Let $|{f(x)}|\le m$ and $x\in \mathbb{X}$. I want to define $f(x)$ as a $f(x) \in \mathcal{B}_{m}(\mathbb{X})$. Is there any such notation?
Pankaj Mishra's user avatar
1 vote
1 answer
49 views

Which expression is correct for using the sign $:=$ in the given problem?

Imagine that I have this limit $$ \lim_{x\to a} f(x)=\frac{b^2-c^3}{8b^2-9c^2+a} ,$$ and I want to denote its RHS by another notation, say, $g$. Then, which notation is correct $$ \lim_{x\to a} f(...
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Rounding error of matrix multiplication when one of the matrices is orthogonal

I am studying Scientific computing from Biswa Nath Datta's Numerical Linear Algebra and Applications and there is a corollary after explaining matrix multiplication rounding error described below. if $...
asha soroushpoor's user avatar
1 vote
2 answers
36 views

Set builder notation for a list of times at which either of two functions have a certain value

I have two functions of time: $f(t)$ and $g(t)$. These functions oscillate over time at different rates. I am hoping to build a set, $S$, that contains all of the times at which $f(t) = X$, as well as ...
MathIsHard's user avatar
0 votes
1 answer
161 views

How To Interpret E+ or E- Notation in Curves of Best Fit?

I have some data which I plotted using google sheets. I came up with a curve of best fit which was a degree 4 polynomial. The equation I got was: 9E+08 + 1.86E+06x + - 1397x^2 + 0.467x^3 - 5.85E-05x^4 ...
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What does E x~y notation mean in functions?

In some articles there is a notation like E x~y , does this "E" mean expected value(mean) or it is referring to something else? for example in this formula, how can I read the first part (E ...
S Roshan's user avatar
-1 votes
1 answer
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what does the notation $x \in \left\{ 0 \right\} \cup \left[ {\begin{array}{*{20}{c}} \delta &1 \end{array}} \right]$ mean?

I am reading Lemma~1.(a) in the paper "A tutorial on modeling and analysis of dynamic social networks. Part II" where it says $w_{ij}(k) \in \left\{ 0 \right\} \cup \left[ {\begin{array}{*{...
Alex Mathy's user avatar
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1 answer
83 views

What is the difference between those tensors

Recently I was studying quantum electrodynamics and got a small question about tensors. The Lagrangian of QED has this thing $\frac{1}{4}F^{\mu \nu}F_{\mu \nu}$ And I can't understand the difference ...
JavaGamesJAR's user avatar
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1 answer
121 views

E in exponential regression equation

Hello I came across an exponential regression equation in excel and I was wondering what did the "E" stand for? the equation is : y=5E-09e^0,0139x 1 Can someone please help me by showing ...
sam's user avatar
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What does the notation $\mathbf{1}_{\{i=l\}}$ mean? [duplicate]

I found this notation in a published article, with no formal definition. I am attaching a screenshot of where it's used. where, $i,l \in \mathcal{N}$. I am guessing $\mathbf{1}_{\{i=l\}}$ denotes a ...
Math101's user avatar
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Mathematical notation of an one hot vectors in ML

I have a vector a vector of length $n$and can only contain values $\{A,B,C\}$. I'm representing this mathematically as: $$\mathbf{x} \in \{A,B,C\}^{1\times n}$$ Question 1: Am I properly ...
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1 vote
1 answer
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Unfamiliar Scientific Notation

I am reading a paper that uses notation like $10^{15\pm1}$ that I have never seen before. I can guess that it means the number is in the interval of $10^{14}$ to $10^{16}$, but I would appreciate it ...
user1930565's user avatar
2 votes
1 answer
1k views

Is there any notation/symbol to indicate a variable as constant?

I was working on some applied differential equations problem in physics, and I was wondering if there was any simple notion to indicate that a variable in an equation is constant (similar to how x ∈ R ...
01penguin's user avatar
3 votes
1 answer
249 views

Explanations of mathematical notation. [duplicate]

I am new to machine learning. I am currently studying various kinds of regressions using the scikit-learn Python library. Here's an example from the documentation: https://scikit-learn.org/stable/...
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2 answers
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Are 3.0, 3.00, 3.000 ... all equal?

This may be too trivial to ask. But when I searched, I didn't find anyone asking this question previously on this site. When I consider 3.0 and 3.00, from a mathematical perspective, absolutely I can ...
Sourav Kannantha B's user avatar
1 vote
1 answer
330 views

In a floating-point system, is the unit roundoff $\epsilon_{mach}$ necessarily a machine number?

I have to answer the following questions: (a)In a floating-point system, is the unit roundoff $\epsilon_{mach}$ necessarily a machine number? (Explain your answer or give a counterexample). (b) Is ...
Alex Turner's user avatar
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1 answer
29 views

Is there an easy way to algebraically manipulate a large exponential value with a base other than 10 into a base of 10 to be more tangible? IE: 3^3778

Quick preface as with my other posts: I'm not a math major, but I'm enjoying the math portion of my studies, so please keep any explanation on an idiot's level lol - thanks! I came across a problem ...
Wayne Roberts's user avatar
1 vote
2 answers
186 views

How to read the symbol $\gtreqqless$?

The book I am currently reading, is written in a local language, uses the symbol $$\gtreqqless$$ Noted usage in the book (translated): Let $f(x) = x^3e^{-3x}$ for x > 0. Then what is the maximum ...
Krosin's user avatar
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1 answer
290 views

How to convert $10^n$ to scientific notation where $n \in \Bbb Q$?

How to convert $10^n$ to scientific notation where $n \in \Bbb Q$? For simplicity take the example $10^{7.44}$. I know how to convert scientific notations to the power of $10$. Like If we want to ...
Mridul Kumar's user avatar
1 vote
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How many of these numbers are written in scientific notation? $\sqrt7\times10^{-20}$, $5.3\times2^{10}$, $(\frac13)^{-1}\times10^{15}$

How many numbers are written in scientific notation? $\sqrt7\times10^{-20}$ $5.3\times2^{10}$ $(\frac13)^{-1}\times10^{15}$ $1)\text{zero}\qquad\qquad2)1\qquad\qquad3)2\qquad\qquad4)3$ We know that ...
Etemon's user avatar
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0 votes
1 answer
805 views

Notation for sampling specific number of samples from distribution

I am in the process of writing a scientific paper. At a certain point I want to mention a sampling operation, namely that a variable hereafter called X is a sample obtained from a distribution T. ...
pilu's user avatar
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0 votes
2 answers
53 views

How to interpret / read the following mathematical notations?

In one of the paper I am reading, I came across two mathematical notations which I cannot understand. The author also did not give any explanation. In both, note that $N$ is a positive integer. Term 1:...
SJa's user avatar
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0 votes
1 answer
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Generalized max function that chooses N largest items.

Let $X$ be a list of real numbers. The length of $X$ is finite, i.e., $|X|=m<\infty$. The largest element of $X$ can be denoted by $\max X$. My question is Is there any mathematical notation that ...
Andeanlll's user avatar
1 vote
2 answers
424 views

Why is 5.93e-56 considered to be close to zero? [closed]

I am very poor in math but have recently been studying some math courses, unfortunately they do not explain things well. I have heard multiple times now that values like ...
PKTN100's user avatar
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0 answers
83 views

Matrices, Vectors and Notation

Let a matrix $\mathbf{G}$ be a function of a vector $\mathbf{x}=\begin{bmatrix}x_1 \\ x_2\end{bmatrix}$: $$ \mathbf{G} = \begin{bmatrix}x_1 & 0 \\ 0 & x_2\end{bmatrix}.$$ I believe it is valid ...
Adeel's user avatar
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0 answers
23 views

Name of the notation $(s|z,u,n)$

what is the name of the notation , I didn't get it (as physics student we call $\langle q|p\rangle$ Braket notation) but in software books i am often seeing that notation how can you call it does it ...
Dev Ran's user avatar
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0 answers
60 views

Scientific notation into binary notation

$0.25E3 = 0.25 \cdot 10^3 = 250$. I am trying to write it in binary notation which should be something like for example if binary is $11111010$ then the binary would be in scientific notation $0....
smoni's user avatar
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2 votes
3 answers
546 views

How to solve a fraction with a numerator in exponential form and a denominator in numerical form without a calculator?

The question: "Imagine unwinding (straightening out) all of the DNA from a single typical cell and laying it "end-to-end"; then the sum total length will be approximately $2$ meters. ...
Matthew S.'s user avatar
0 votes
2 answers
17k views

What does 3.199E +01 mean? [duplicate]

What is the exact value of 3.199 E +01 ? Does it mean $3.199\times10^1$?? I get confused with the notation.
Pramod's user avatar
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1 vote
4 answers
42 views

$N × 10^a$ notation

Today our teacher taught us the $N × 10^a$ notation. He specified that $N$'s value must be $1 ≤ N < 10$ and that $a$ must be an integer. I understood that much but I was wondering, why can't $N$ ...
iaminsensible's user avatar
2 votes
2 answers
7k views

How to interpret scientific notation?

I'm having a problem understanding scientific notation. What is the difference between the following: $$\text{5e2, 5e-2, -5e2, -5e-2}$$
user01101001's user avatar
7 votes
1 answer
9k 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., $0=0×10^0=0×...
user 85795's user avatar
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9 votes
5 answers
31k views

Scientific notation and negative numbers

My daughter is learning scientific notation in school, and her textbook says something to the effect of this: Scientific notation is a method of writing numbers as the product of two factors where ...
Yishai's user avatar
  • 715
62 votes
3 answers
479k views

What does E mean in 9.0122222900391E-5? [closed]

I often find this at the bottom of pages. Page generated in 0.00013899803161621 Sometimes, I come across Page generated in 9.0122222900391E-5 What does that time mean? I tried searching Wikipedia ...
abel's user avatar
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