Algebra Tutorials!  
     
     
Monday 26th of June
   
Home
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
Mixed
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Algebra
Order of Operations
Dividing Complex Numbers
Polynomials
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Factoring
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Numbers
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Fractions
Polynomials
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Exponents
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Radicals
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
   
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Powers of ten (Scientific Notation)

In so-called scientific notation , numbers are written as a product of two parts:

(i) a number between 1 and 9.9999…..

and

(ii) a power of 10.

To convert a number to scientific notation, just move the decimal point from its initial position until it is just to the right of the first nonzero digit. The number of positions you move the decimal point gives the numerical value of the power of 10 required. If the decimal point was moved to the left, the power of 10 is positive. If the decimal point was moved to the right, the power of 10 is negative.

Examples:

(Note that 4.3257 × 10 3 = 4.3257 × 1000 = 4325.7, demonstrating that the scientific notation form is the same numerical value as the original number.)

(Note that 5.93 × 10 -3 = 5.93 × 0.001 = 0.00593, demonstrating that the scientific notation form is the same numerical value as the original number.)

(Note that -7.5 × 10 8 = -7.5 × 100,000,000 = -750,000,000, demonstrating that the scientific notation form is the same numerical value as the original number.)

(Note that -3.6 × 10 -8 = -3.6 × 0.00000001 = -0.000000036, demonstrating that the scientific notation form is the same numerical value as the original number.)

Notice that the number itself can be positive or negative and the exponent on the 10 can be positive or negative, and that these two signs are quite independent of each other.

Obviously, to convert back from scientific notation to ordinary decimal numbers, you just move the decimal point the number of places left or right as indicated by the power of 10.

Examples:

(Or, using ordinary arithmetic, 5.96953 × 10 4 = 5.96953 × 10,000 = 59695.3.)

(Or, using ordinary arithmetic, 7.353 × 10 -6 = 7.353 × 0.000001 = 0.000007353.)

(Or, using ordinary arithmetic, -2.3 × 10 2 = -2.3 × 100 = -230.)

(Or, using ordinary arithmetic, -3.592 × 10 -3 = -3.592 × 0.001 = -0.003592.)

To help you remember these rules, just keep in mind that when the power of 10 is positive, the original numerical value was bigger than 1. When the power of 10 is negative, the original numerical value was a fraction, smaller than 1. The rules are not something new or mysterious. As shown in brackets following each example above, the rules just reflect simple numerical properties – they produce the result of ordinary multiplication by powers of 10.

If you have a scientific calculator capable of handling scientific notation, then entry of such numbers is straightforward. First key in the numerical part. Then press a key (typically it has an upper case ‘E’ on it) and key the exponent. You could use the above example as a test case for checking to see that you know how to enter numbers in scientific notation into your calculator.

Remark 1:

The use of scientific notation solves the problem of how to distinguish between trailing zeros in whole numbers which are significant, and those which are present only to tell us where the decimal point is located (and so are not significant digits). (To review the nature of this problem, just re-read the previous document on significant digits.)

When we use scientific notation, there can be no trailing zeros to the left of the decimal point. The only trailing zeros in a number in scientific notation are to the right of the decimal point, and therefore are automatically significant digits, according to the rules.

So, for example

32000 is written 3.2 × 10 4 if none of the three zeros are significant.

32000 is written 3.20 × 10 4 if just the first of the three zeros is significant, but the remaining two zeros are present only to locate the decimal point.

32000 is written 3.200 × 10 4 if just the first two of the three zeros are significant, but the third zero is present only to locate the decimal point. 32000 is written

3.2000 × 10 4 if all three zeros are significant.

 
Copyrights © 2005-2017