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Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Angles and Degree Measure
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Scientific notation


In engineering calculations numbers are often very small or very large, for example 0.00000345 and 870,000,000. To avoid writing lengthy strings of numbers a notation has been developed, known as scientific notation which enables us to write numbers much more concisely.

1. Scientific notation

In scientific notation each number is written in the form

a × 10

where a is a number between 1 and 10 and n is a positive or negative whole number. Some numbers in scientific notation are

5×10, 2.67×10, 7.90×10

To understand scientific notation you need to be aware that 10 = 10, 10 = 100, 10 = 1000, 10 = 10000 and so on, and also that

and so on.

You also need to remember how simple it is to multiply a number by powers of 10. For example to multiply 3.45 by 10, the decimal point is moved one place to the right to give 34.5. To multiply 29.65 by 100, the decimal point is moved two places to the right to give 2965. In general, to multiply a number by 10 the decimal place is moved n places to the right if n is a positive whole number and n places to the left if n is a negative whole number. It may be necessary to insert additional zeros to make up the required number of digits.


The following numbers are given in scientific notation. Write them out fully.

a) 5×10

b) 2.67×10

c) 7.90×10


a) 5×10 = 5×1000 = 5000.

b) 2.67×10 = 26700

c) 7.90×10 = 0.00790


Express each of the following numbers in scientific notation.

a) 5670000

b) 0.0098


a) 5.67×10

b) 9.8×10


1. Express each of the following in scientific notation.

a) 0.00254

b) 82

c) -0.342

d) 1000000


1. a) 2.54×10, b) 8.2×10, c) -3.42×10, d) 1×10 or simply 10

2. Using a calculator

Students often have difficulty using a calculator to deal with scientific notation. You may need to refer to your calculator manual to ensure that you are entering numbers correctly. You should also be aware that your calculator can display a number in lots of different forms including scientific notation. Usually a MODE button is used to select the appropriate format. Commonly the EXP button is used to enter numbers in scientific notation. (EXP stands for exponent which is another name for a power). A number like 3.45×10 is entered as 3.45 EXP 7 and might appear in the calculator window as 3.45. Alternatively your calculator may require you to enter the number as 3.45E7 and it may be displayed in the same way. You should seek help if in doubt.

Computer programming languages use similar notation. For example

8.25 ×10 may be programmed as 8.25E7


9.1×10 may be programmed as 9.1E-3

Again, you need to take care and check the required syntax carefully.

A common error is to enter incorrectly numbers which are simply powers of 10. For example, the number 10 is erroneously entered as 10E7 which means 10×10, that is 10. The number 10, meaning 1×10, should be entered as 1E7.

Check that you are using your calculator correctly by verifying that

(3×10)×(2.76×10)×(10) = 8.28×10

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