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Scientific Notation
Scientific notation expresses a very large or small number as
Learning Objective

Practice calculations with numbers in scientific notation and explain why scientific notation is useful
Key Points
 Scientific notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form.
 In normalized scientific notation, the exponent
$n$ is chosen so that the absolute value of a remains at least 1 but less than 10$\left ( 1 \leq \left  m \right  < 10 \right )$ .  When numbers written in scientific notation are involved in multiplication or division, the standard rules for operations with exponentiation apply. When addition or subtraction is involved, the number must first be rewritten so the exponent is the same.
 Most calculators present very large and very small results in scientific notation. Because superscripted exponents like
$10^7$ cannot always be conveniently displayed, the letter E or e is often used to represent "times ten raised to the power of" (which would be written as "$\cdot 10^b$ ").
Terms

Scientific notation
A method of writing or of displaying real numbers as a decimal number between 1 and 10 followed by an integer power of 10.

normalized scientific notation
A number written in scientific notation
$m \cdot 10^n$ such that the absolute value of$m$ remains at least 1 but less than 10.
Full Text
Scientific notation, also known as standard form, is way to conveniently write numbers that are very large or very small. This method is commonly used by mathematicians, scientists, and engineers.
For example, the number
Scientific notation is written as follows, read "m times 10 raised to the power of n."
Writing a Number in Scientific Notation
To write a number in scientific notation:
 Move the decimal point so that there is one nonzero digit to its left.
 Multiply the result by a power of 10 using an exponent whose absolute value is the number of places the decimal point was moved. Make the exponent positive if the decimal point was moved to the left and negative if the decimal point was moved to the right.
Let's write the number 43,500 in scientific notation. The decimal should be moved 4 places to the left, so the number can be rewritten as follows:
A number written in scientific notation can be converted to standard form by reversing the process described above. For example, let's write the number
Normalized Scientific Notation
Any given number can be written in the form of
In normalized scientific notation, the exponent
Following these rules, 350 would always be written as
Normalized scientific form is the typical form of expression for large numbers in many fields, except during intermediate calculations or when an unnormalized form, such as engineering notation, is desired. Normalized scientific notation is often called exponential notation—although the latter term is more general and also applies when
Calculations involving Scientific Notation
When numbers written in scientific notation are multiplied or divided, the standard rules for operations with exponentiation apply. For example:
When numbers written in scientific notation are added or subtracted, the numbers first must be rewritten so the exponents are be the same. Then, the constant value, or
E Notation
Most calculators and many computer programs present very large and very small results in scientific notation. Because superscripted exponents like
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Key Term Reference
 absolute value
 Appears in these related concepts: Inequalities with Absolute Value, Piecewise Functions, and Equations with Absolute Value
 base
 Appears in these related concepts: Changing Logarithmic Bases, Logarithms of Powers, and Rational Exponents
 constant
 Appears in these related concepts: Inverse Variation, Graphing Quadratic Equations in Vertex Form, and Direct Variation
 e
 Appears in these related concepts: Natural Logarithms, The Number e, and Common Bases of Logarithms
 exponent
 Appears in these related concepts: Logarithms of Products, Logarithms of Quotients, and Rules for Exponent Arithmetic
 exponential
 Appears in these related concepts: Exponential Growth and Decay, Solving General Problems with Logarithms and Exponents, and Population Growth
 exponential function
 Appears in these related concepts: Interest Compounded Continuously, Graphs of Exponential Functions, Base e, and Basics of Graphing Exponential Functions
 exponentiation
 Appears in these related concepts: Introduction to Exponents, Radical Functions, and Logarithmic Functions
 expression
 Appears in these related concepts: Compound Inequalities, Sets of Numbers, and Graphs of Equations as Graphs of Solutions
 function
 Appears in these related concepts: Solving Differential Equations, Visualizing Domain and Range, and The Vertical Line Test
 point
 Appears in these related concepts: Graphing Quadratic Equations In Standard Form, Graphing Equations, and Polynomial and Rational Functions as Models
 range
 Appears in these related concepts: Introduction to Domain and Range, Inverse Functions, and The Derivative as a Function
 sign
 Appears in these related concepts: The Intermediate Value Theorem, The Rule of Signs, and Polynomial Inequalities
 term
 Appears in these related concepts: Basics of Graphing Polynomial Functions, The 22nd Amendment, and Introduction to Variables
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Cite This Source
Source: Boundless. “Scientific Notation.” Boundless Algebra. Boundless, 27 May. 2016. Retrieved 27 Jul. 2016 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/numbersandoperations1/furtherexponents13/scientificnotation664740/