scientific notation

Examples of scientific notation in the following topics:

• Scientific Notation

  • Therefore, they can be rewritten as a power of 10 using scientific notation.
  • For example, let's write the number 43,500 in scientific notation.
  • In normalized scientific notation, also called exponential notation, the exponent $n$ is chosen so that the absolute value of $m$ remains at least 1 but less than 10.
  • Note that in this usage, the character e is not related to the mathematical constant $\mathbf{e}$ or the exponential function $e^x$ (a confusion that is less likely if a capital E is used), and though it stands for exponent, the notation is usually referred to as (scientific) E notation or (scientific) e notation, rather than (scientific) exponential notation.
  • Practice calculations with numbers in scientific notation and explain why scientific notation is useful

• Series and Sigma Notation

  • Sigma notation, denoted by the uppercase Greek letter sigma $\left ( \Sigma \right ),$ is used to represent summations—a series of numbers to be added together.
  • One way to compactly represent a series is with "sigma notation," or "summation notation," which looks like this: $\displaystyle{\sum _{n=3}^{7}{n^2}}$ .
  • To "unpack" this notation, $n=3$ represents the number at which to start counting ($3$), and the $7$ represents the point at which you stop.

• Equations and Inequalities

  • The notation $a \neq b$ means that a is not equal to $b$.
  • The notation $a < b$ means that a is less than $b$.
  • The notation $a > b$ means that a is greater than $b$.
  • The notation $a \leq b$ means that $a$ is less than or equal to $b$ (or, equivalently, not greater than $b$, or at most $b$).
  • The notation $a \geq b$ means that $a$ is greater than or equal to $b$ (or, equivalently, not less than $b$, or at least $b$).

• Interval Notation

  • Interval notation uses parentheses and brackets to describe sets of real numbers and their endpoints.
  • Use interval notation to show how a set of numbers is bounded

• Graphical Representations of Functions

  • Function notation, $f(x)$ is read as "$f$ of $x$" which means "the value of the function at $x$."  
  • Since the output, or dependent variable is $y$, for function notation often times $f(x)$ is thought of as $y$.  
  • The ordered pairs normally stated in linear equations as $(x,y)$, in function notation are now written as $(x,f(x))$.

• Introduction to Inequalities

  • Strict inequalities differ from the notation $a \neq b$, which means that a is not equal to $b$.
  • The notation $a < b$ means that a is less than $b$.
  • The notation $a > b$ means that a is greater than $b$.
  • The notation $a \leq b$ means that $a$ is less than or equal to $b$ (or, equivalently, not greater than $b$, or at most $b$).
  • The notation $a \geq b$ means that $a$ is greater than or equal to $b$ (or, equivalently, not less than $b$, or at least $b$).

• Functions and Their Notation

  • Another commonly used notation for a function is $f:X\rightarrow Y$, which reads as saying that $f$ is a function that maps values from the set $X$ onto values of the set $Y$.
  • Connect the notation of functions to the notation of equations and understand the criteria for a valid function

• Absolute Value

  • The notation $\left | a \right |$ was introduced by Karl Weierstrass in 1841.

• Simplifying Algebraic Expressions

  • Algebraic notation follows certain rules and conventions, and has its own terminology.

• What is a Matrix?

  • An English mathematician named Cullis was the first to use modern bracket notation for matrices in $1913$ and he simultaneously demonstrated the first significant use of the notation $A=a_{i,j}$ to represent a matrix where $a_{i,j}$ refers to the element found in the ith row and the jth column.