Algebra Tutorials!    
         
  Friday 19th of October      
 
   
Home
Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Decimals
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
Equations
   
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.


Scientific Notation

Many of the numbers that are encountered in science are either very large or very small. For example, the distance from the earth to the sun is 93,000,000 miles, and a hydrogen atom weighs 0.0000000000000000000000017 gram. Scientific notation provides a convenient way of writing very large and very small numbers. In scientific notation the distance from the earth to the sun is 9.3 × 107 miles and a hydrogen atom weighs 1.7 × 10-24 gram. In scientific notation the times symbol, , is used to indicate multiplication. Converting a number from scientific notation to standard notation is simply a matter of multiplication.

 

Example 1

Scientific notation to standard notation

Write each number using standard notation.

a) 7.62 × 105

b) 6.35 × 10-4

Solution

a) Multiplying a number by 105 moves the decimal point five places to the right:

b) Multiplying a number by 10-4 or 0.0001 moves the decimal point four places to the left:

The procedure for converting a number from scientific notation to standard notation is summarized as follows.

 

Strategy for Converting from Scientific Notation to Standard Notation

1. Determine the number of places to move the decimal point by examining the exponent on the 10.

2. Move to the right for a positive exponent and to the left for a negative exponent.

 

A positive number in scientific notation is written as a product of a number between 1 and 10, and a power of 10. Numbers in scientific notation are written with only one digit to the left of the decimal point. A number larger than 10 is written with a positive power of 10, and a positive number smaller than 1 is written with a negative power of 10. Numbers between 1 and 10 are usually not written in scientific notation. To convert to scientific notation, we reverse the strategy for converting from scientific notation.

 

Strategy for Converting from Standard Notation to Scientific Notation

1. Count the number of places (n) that the decimal point must be moved so that it will follow the first nonzero digit of the number.

2. If the original number was larger than 10, use 10n.

3. If the original number was smaller than 1, use 10-n.

 

Example 2

Standard notation to scientific notation

Convert each number to scientific notation.

a) 934,000,000

b) 0.0000025

Solution

a) In 934,000,000 the decimal point must be moved eight places to the left to get it to follow 9, the first nonzero digit.

934,000,000 = 9.34 × 108 Use 8 because 934,000,000 > 10.

b) The decimal point in 0.0000025 must be moved six places to the right to get the 2 to the left of the decimal point.

0.0000025 = 2.5 × 10-6 Use -6 because 0.0000025 < 1.

We can perform computations with numbers in scientific notation by using the rules of exponents on the powers of 10.

 

Example 3

Using scientific notation in computations

Evaluate by first converting each number to scientific notation.

Solution

 
  Commutative and associative properties
  = 0.5 × 105  
  = 5 × 10-1 × 105 Write 0.5 in scientific notation.
  = 5 ×104  
Copyrights © 2005-2018