Scientific Notation SLIDE SHOW INSTRUCTIONS To move forward in the presentation press the ‘right arrow’ button (Page down or enter also work) To move backward press the ‘left arrow’ button To exit the presentation, press ‘escape’ (ESC, top left of keyboard) Copyright © 2011 Lynda Greene Aguirre

Table of Contents Concepts & Definitions Click on links to skip to each section listed Concepts & Definitions Change Scientific to Standard Notation Change Standard to Scientific Notation Special Cases Practice Problems Copyright © 2011 Lynda Greene Aguirre

Copyright © 2011 Lynda Greene Aguirre Concepts and Definitions Copyright © 2011 Lynda Greene Aguirre

Why use Scientific Notation? In scientific applications, there are often very large or very small numbers such as these Very large number: 53,000,000,000,000,000 Very small number: 0.000000000000418 Note: The numbers above are written in STANDARD NOTATION Copyright © 2011 Lynda Greene Aguirre

Why use Scientific Notation? Trying to do calculations using such long numbers can be time consuming. So a different way of writing these numbers was developed which is commonly called scientific notation. Also called “exponential notation” in some textbooks Copyright © 2011 Lynda Greene Aguirre

Why use Scientific Notation? The process (in a nutshell) is to shorten the number by changing the long string of leading or trailing zeros into a power of 10. 53,000,000,000,000,000 “trailing” zeros 0.000000000000418 “leading” zeros Copyright © 2011 Lynda Greene Aguirre

Scientific Notation Positive powers create “trailing” digits Question: Why use a power of 10? Positive powers create “trailing” digits Note: Each new zero actually represents a decimal place, it might not be the number “zero” when you are using it in calculations. The power on the ten is the same as the number of zeros on the right. Answer: You can use it to move the decimal point to the right. Copyright © 2011 Lynda Greene Aguirre

Scientific Notation Question: Why use a power of 10? Negative Powers create “leading” digits If you line up the “1”s, notice that each negative power moves the decimal point to the left of its previous position Answer: You can use it to move the decimal point to the left. Copyright © 2011 Lynda Greene Aguirre

What does Scientific Notation look like? Positive or negative sign indicates BIG or SMALL number Format: THE EXPONENT THE COEFFICIENT Multiplication symbol Note: If the coefficient has a decimal point after the first digit, it is called “normalized”. The position of the decimal point does not change any mathematical procedures Copyright © 2011 Lynda Greene Aguirre

A missing decimal point means it’s to the right of the coefficient. The following numbers are all written in scientific notation A missing decimal point means it’s to the right of the coefficient. (2 means 2.0) Parentheses are sometimes used to indicate multiplication Negative power means it’s a very small number Many calculators show scientific notation this way Zeros in between non-zero digits are included in the coefficient EE3 means 10 to the third power The decimal might not be after the first digit Copyright © 2011 Lynda Greene Aguirre

430,000,000 Is it a Positive or Negative Power? Big numbers with TRAILING ZEROS have a positive power (usually not shown). 430,000,000 Trailing Zeros will have no sign on the power No sign HERE means it’s positive Copyright © 2011 Lynda Greene Aguirre

Positive or Negative Sign? Small numbers with LEADING ZEROS have a negative power 0.00000043 Leading Zeros will have a negative power on the “10” Copyright © 2011 Lynda Greene Aguirre

Scientific Notation Moving the decimal point Note: A decimal point to the right of any number does not have to be included Decimal moved from HERE 5 digits to the right To HERE Copyright © 2011 Lynda Greene Aguirre

Changing from Scientific Notation into Standard Notation Copyright © 2011 Lynda Greene Aguirre

Step by Step Process 1. Write down the coefficient Positive power - move right The power of ten tells you how far to move 2. Move decimal point two places to the right You can drop the decimal point if it’s to the right of the last digit Note: You may need to fill in some zeros if there are not enough digits in the original number Copyright © 2011 Lynda Greene Aguirre

Step by Step Process POSITIVE power Write down the coefficient Move the decimal point six places to the right Fill in some zeros if there are not enough digits in the original number Drop the decimal point if it’s behind the last digit Copyright © 2011 Lynda Greene Aguirre

Step by Step Process POSITIVE power Write down the coefficient Move the decimal point four places to the right Fill in some zeros if there are not enough digits in the original number Drop the decimal point if it’s behind the last digit Copyright © 2011 Lynda Greene Aguirre

Step by Step Process POSITIVE power Write down the coefficient Move the decimal point two places to the right No need to fill in zeros. There are enough digits in the original number Keep the decimal point because it’s not behind the last digit Copyright © 2011 Lynda Greene Aguirre

Step by Step Process Look at the NEGATIVE power NOTE: Leave room on the left side to move the decimal Write down the coefficient Move the decimal point three places to the LEFT Fill in some zeros if there are not enough digits in the original number Keep the decimal point because it’s not behind the last digit Copyright © 2011 Lynda Greene Aguirre

Step by Step Process NEGATIVE power Write down the coefficient Move the decimal point three places to the LEFT Fill in zeros Keep the decimal point because it’s not behind the last digit Copyright © 2011 Lynda Greene Aguirre

Step by Step Process NEGATIVE power Write down the coefficient NOTE: Leave room on the left to move the decimal Move the decimal point four places to the LEFT Fill in zeros Keep the decimal point because it’s not behind the last digit Copyright © 2011 Lynda Greene Aguirre

Step by Step Process NEGATIVE power Write down the coefficient Move the decimal two places to the LEFT Fill in zeros Keep the decimal point because it’s not behind the last digit Practice Problems Table of contents Copyright © 2011 Lynda Greene Aguirre

Step by Step Process NEGATIVE power 1. Write down the coefficient Move the decimal point one place to the LEFT 3. No need to fill in zeros. There are enough digits in the original number Keep the decimal point because it’s not behind the last digit Copyright © 2011 Lynda Greene Aguirre

Changing from Scientific Notation into Standard Notation Special Cases Copyright © 2011 Lynda Greene Aguirre

Zero power This is the answer ZERO power 1. Write down the coefficient 2. Decimal point doesn’t need to be moved Copyright © 2011 Lynda Greene Aguirre

No Decimal on Coefficient Note: If the coefficient does not have a decimal point visible, it is “understood” to be to the right of it. REWRITE THE COEFFICIENT TO SHOW THE POSITION OF THE DECIMAL POINT Copyright © 2011 Lynda Greene Aguirre

No Decimal on Coefficient POSITIVE power 1. Write down the coefficient Move 3 places to the right Fill in zeros Drop the decimal point if it’s behind the last digit Copyright © 2011 Lynda Greene Aguirre

Calculator Format Note: If a different format of scientific notation is used, you can change the format or work the problem in its original form YOU CAN REWRITE THE PROBLEM IN NORMALIZED FORM Copyright © 2011 Lynda Greene Aguirre

Calculator Format POSITIVE power 1. Write down the coefficient Move 3 places to the right Fill in zeros Drop the decimal point if it’s behind the last digit Copyright © 2011 Lynda Greene Aguirre

Different Multiplication Format Note: If a different format of scientific notation is used, you can change the format or work the problem in its original form YOU CAN REWRITE THE PROBLEM IN NORMALIZED FORM Copyright © 2011 Lynda Greene Aguirre

Different Multiplication Format Example: POSITIVE power 1. Write down the coefficient Move 3 places to the right Fill in zeros Drop the decimal point if it’s behind the last digit Practice Problems Table of contents Copyright © 2011 Lynda Greene Aguirre

Changing from Standard Notation into Scientific Notation Copyright © 2011 Lynda Greene Aguirre

Review Number Type Location of zeros Sign of the Power SMALL NUMBERS (decimal places) Sign of the Power SMALL NUMBERS left side of the coefficient negative power BIG NUMBERS right side of the coefficient positive power Error Prevention Tip: Knowing where the zeros belong will prevent students from moving the decimal in the wrong direction Copyright © 2011 Lynda Greene Aguirre

Standard to Scientific Notation Now that we know how to do this process in one direction, it is simple to reverse it. The zeros are on the right hand side, so the power will be positive The coefficient includes everything except the trailing zeros Copyright © 2011 Lynda Greene Aguirre

Standard to Scientific Notation Write the coefficient in normalized form (i.e. decimal point after the first digit) 2. Write “x 10” next to it (i.e.the power of ten) Copyright © 2011 Lynda Greene Aguirre

Standard to Scientific Notation 3. This is a big number, so the power will be positive Note: You can omit the “+” sign if you like, but it’s not wrong to write it down Copyright © 2011 Lynda Greene Aguirre

Count decimal places This gives us the power: +8 Decimal point was not showing, which means it’s behind the last digit 4. Count the number of digits between the new position and its old position Decimal moved from HERE To HERE There are 8 digits between the new and old positions This gives us the power: +8 Copyright © 2011 Lynda Greene Aguirre

Putting the pieces together Write the coefficient in Normalized Form (decimal point after the first digit) 2. Write “x 10” next to it Sign of the power? zeros on the right?-positive zeros on the left?-negative 4. How far did the decimal point move? (count digits between old and new decimal points) Copyright © 2011 Lynda Greene Aguirre

Putting the pieces together Extra digits are to the RIGHT of the coefficient Write the coefficient in Normalized Form + 6 3. Sign of the power? 2. Write “x 10” next to it 4. How far did the decimal point move? There are 6 digits between the new and old positions Copyright © 2011 Lynda Greene Aguirre

Putting the pieces together Extra digits are to the LEFT of the coefficient Write the coefficient in Normalized Form - 4 3. Sign of the power? 2. Write “x 10” next to it 4. How far did the decimal point move? There are 4 digits between the new and old positions Copyright © 2011 Lynda Greene Aguirre

Putting the pieces together Extra digits are to the RIGHT of the coefficient Write the coefficient in Normalized Form + 8 3. Sign of the power? 2. Write “x 10” next to it 4. How far did the decimal point move? There are 8 digits between the new and old positions Copyright © 2011 Lynda Greene Aguirre

Putting the pieces together Extra digits are to the LEFT of the coefficient Write the coefficient in Normalized Form - 2 3. Sign of the power? 2. Write “x 10” next to it 4. How far did the decimal point move? There are 2 digits between the new and old positions Practice Problems Table of contents Copyright © 2011 Lynda Greene Aguirre

Copyright © 2011 Lynda Greene Aguirre Practice Problems Copyright © 2011 Lynda Greene Aguirre

Copyright © 2011 Lynda Greene Aguirre Practice Problems A Copyright © 2011 Lynda Greene Aguirre

Copyright © 2011 Lynda Greene Aguirre Practice Problems B Copyright © 2011 Lynda Greene Aguirre

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