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Scientific Notation
Scientific notation expresses a number as
Learning Objective

Express numbers in scientific notation and standard notation
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 b is chosen so that the absolute value of a remains at least one but less than ten
$\left ( 1 \leq \left  a \right  < 10 \right )$ .  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 "$\cdot 10^b$ ").
Term

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.
Example
Full Text
Standard Form to Scientific Form
Very large numbers such as
To see how this is done, let us start with a somewhat smaller number such as 2480.
Standard Form Versus Scientific Form
In standard form, the number is written out as you are accustomed to, the ones digit to the farthest to the right (unless there is a decimal), then the tens digit to the left of the ones, and so on. In scientific notation, a number in standard notation with one nonzero digit to the left of the decimal is multiplied by ten to some power, as shown.
The last form in is called the scientific form of the number. There is one nonzero digit to the left of the decimal point and the absolute value of the exponent on 10 records the number of places the original decimal point was moved to the left. If instead we have a very small number, such as
There is one nonzero digit to the left of the decimal point and the absolute value of the exponent of 10 records the number of places the original decimal point was moved to the right.
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.
A number written in scientific notation can be converted to standard form by reversing the process described above.
Normalized Scientific Notation
Any given number can be written in the form of
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: Piecewise Functions, Introduction to Absolute Value, and Equations with Absolute Value
 base
 Appears in these related concepts: Logarithms of Powers, Balancing Redox Equations, and Strong Bases
 constant
 Appears in these related concepts: Inverse Variation, Quadratic Functions of the Form f(x) = a(xh)^2 + k, and Direct Variation
 e
 Appears in these related concepts: Derivatives of Exponential Functions, Derivatives of Logarithmic Functions, and The Natural Exponential Function: Differentiation and Integration
 exponent
 Appears in these related concepts: Logarithmic Functions, Logarithms of Products, and Scientific Notation
 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: Further Transcendental Functions, Interest Compounded Continuously, and Basics of Graphing Exponential Functions
 expression
 Appears in these related concepts: Simplifying, Multiplying, and Dividing, Compound Inequalities, and Expressions and Sets of Numbers
 function
 Appears in these related concepts: Inverse Functions, Solving Differential Equations, and Functions and Their Notation
 integer
 Appears in these related concepts: Scientific Notation, Total Number of Subsets, and Finding a Specific Term
 point
 Appears in these related concepts: Quadratic Functions of the Form f(x) = ax^2 + bx + c, Where a is not Equal to 0, Graphing Equations, and Introduction: Polynomial and Rational Functions and Models
 range
 Appears in these related concepts: 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 Democracy
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Cite This Source
Source: Boundless. “Scientific Notation.” Boundless Algebra. Boundless, 14 Mar. 2016. Retrieved 30 Apr. 2016 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/thebuildingblocksofalgebra1/exponentsscientificnotationandtheorderofoperations10/scientificnotation664740/