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SCIENTIFIC NOTATION DAY 1 • Learn Vocabulary Terms • Identify Vocabulary terms in problems • Understand why Scientific Notation is used • Identify numbers written in Scientific notation & be able to explain why or why not SCIENTIFIC NOTATION VOCABULARY Scientific Notation: A way of expressing very large or very small numbers more easily using a power of 10 EX: 35,700 = 3.57 x 104 Standard Form: EX: 35,700 The “normal” regular way we write a number SCIENTIFIC NOTATION VOCABULARY Finite decimal: every whole number EX: 5, 78, 90 (any number between 1 & 9) Leading digit: the leftmost digit : single, NON-ZERO number to the left of the decimal EX: 6.5 9.0 Order of magnitude: 2.34 The exponent used to show the power (magnitude of 10) It basically tells us how many times to move the decimal left or right. EX: 105 = 1.00000 http://www.mathsisfun.com/numbers/scientific-notation.html HOW DO I KNOW IF IT’S SCIENTIFIC NOTATION? 1) Must be written as a PRODUCT (X’s) EX: 3.6 x 103 2) The LEADING DIGIT must to the left of the decimal and be a WHOLE number between 1 & 9 EX: 3.6 x 103 3) There must be a order of magnitude (power of 10) EX: 3.6 x 103 EXIT TICKET • IDENTIFY : Leading digit Order of magnitude Product sign 7.8 x 6 10 SCIENTIFIC NOTATION DAY 2 & 3 • Identifying large vs. small numbers by the placement of the zeros. • Using zero placement to tell us which direction the decimal is moved from the leading digit • Identify if the power of 10 is positive or negative by the zeros • Know why we use it DO NOW WHICH NUMBER IS THE SMALLER NUMBER & WHICH NUMBER IS THE LARGER NUMBER? 0.000000089 OR 8,000,000 BE PREPARED TO EXPLAIN/SHARE YOUR CHOICES. SCIENTIFIC NOTATION BASICS • Scientific Notation is a way of expressing very large or very small numbers in an easier way. Large numbers often have MANY zeros at the end. EX: 450,000,000 Small numbers have the zeros at the beginning. EX: 0.000000032 VERY SMALL OR VERY LARGE • Identify each number as very small or very large: 1) 0.000015 SMALL LARGE 2) 6,000,000 SMALL LARGE 3) 0.00000901 SMALL LARGE USE/THINK ABOUT WHAT YOU ALREADY KNOW… • What do you already know about the placement of these zeros? • What does the direction (left; before OR right; after) they tell us about the numbers? • HINT: Think about the number line or the decimal place value chart WE KNOW…… *ALL of these will help you understand SCIENTIFIC NOTATION!!! DO NOW 1) Please write HW in your planners 2) With the people at your tables, complete the review sheet on your desks. REVIEW Vocabulary: Match the term with its definition. ____large numbers A) have zeros at the beginning ____ leading digit B) exponent that shows power of 10 ____ order of magnitude C) have zeros at the end ____ small number D) leftmost digit : single, NON-ZERO number to the left of the decimal Use the expression below to answer the questions: 7.98 x 10 6 The 7 is called the _________________ 10 6 is the ______________ The “x” is the _____________ PRODUCT WORD BANK ORDER OF MAGNITUDE leading digit IDENTIFY which is NOT written in scientific notation and give a reason why 06.9 x 103 9.7 x 52 7.89 x 104 Identify each number as very small or very large: 1) 0.000025 SMALL LARGE 2) 9,000,000 SMALL LARGE 3) 0.00000745 SMALL LARGE Writing numbers in Scientific Notation • Identifying large vs. small numbers by the placement of the zeros. • Using zero placement to tell us which direction the decimal is moved from the leading digit • Identify if the power of 10 is positive or negative by the zeros How to Do it: Writing large numbers in Scientific Notation • To figure out the power of 10, think "how many places do I move the decimal point?“ • If the number is 10 or greater, the decimal point has to move to the left, and the power of 10 will be positive; large number VIDEO http://learnzillion.com/lessons/1177-write-large-numbers-in-scientific-notation EXAMPLE: Write 4,250,000,000 in scientific notation 4.250000000. 4.250000000. 9 places 4.25 x 109 Move the decimal so that only 1 digit is to the left of the decimal Count the number of spaces that the decimal has to be moved to the RIGHT. Write the number WITHOUT ending the zeros, & multiply by the correct power of 10 Let’s PRACTICE Write each number in scientific notation: 1) 68,000 2) 73,280,000 How to Do it: Writing Small numbers in Scientific Notation • To figure out the power of 10, think "how many places do I move the decimal point?“ • If the number is smaller than 1, the decimal point has to move to the right, so the power of 10 will be negative; small number VIDEO http://learnzillion.com/lessons/1255-write-small-numbers-in-scientific-notation EXAMPLE: Write 0.0000000425 in scientific notation 0.00000004.25 Move the decimal so that only 1 NON ZERO digit is to the left of the decimal 0.00000004.25 Count the number of spaces that the decimal has to be moved to the LEFT. 8 places 4.25 x 10-8 Write the number WITHOUT beginning the zeros, & multiply by the correct power of 10 AND use a NEGATIVE exponent to move the decimal to the left. Let’s PRACTICE Write each number in scientific notation: 1) 0.0038 2) 0.0000004 Check! After putting the number in Scientific Notation, just check that: • The "digits" part is between 1 and 10 (it can be 1, but never 10) • The "power" part shows exactly how many places to move the decimal point EXIT TICKET Write the following in scientific notation: 1) 53,000 _______________ 2) 0.0082 _______________ Name:_______________________ Date:_____________________ CLASSWORK M1L9 BASIC SCIENTIFIC NOTATION LEFT NEGATIVE RIGHT POSITIVE Write each number in scientific notation: ORIGINAL NUMBER PLACE DECIMAL & MOVE IN CORRECT DIRECTION FINAL ANSWER 420,000 0.002 4.2 0 0 0 0 4.2 x 105 2 x 10-3 30,000,000 0.00037 804,000,000 13,060,000,000,000 0.0000506 0.000000005507 45,000,000 5,840,000 0 .0 0 2 . SCIENTIFIC NOTATION DAY 4 & 5 • Use knowledge of decimal movement & scientific notation to convert : • Convert FROM scientific notation TO standard form with positive & negative exponents HOW TO USE THE CALCULATOR 1) On 2) Clear 3) Enter the standard form number 4) Press blue “2nd “ key 5) Press “DRG” ( SCI/ENG) 6) Using the right/left arrow keys choose: “FLO” for standard form “ SCI” for scientific notation *if you want to go back to choose another form repeat steps 5 and 6 and then press enter twice http://www.youtube.com/watch?v=BW55IniDb2g&list=PL698BE8091CA9C622 SCIENTIFIC NOTATION VOCABULARY Scientific Notation: A way of expressing very large or very small numbers more easily using a power of 10 EX: 35,700 = 3.57 x 104 Standard Form: EX: 35,700 The “normal” regular way we write a number CONVERTING FROM SCIENTIFIC NOTATION TO STANDARD FORM It’s EASY!!!! ALL you do is work BACKWARDS… SMARTEXCHANGE EXAMPLE: WITH A POSITIVE EXPONENT Write 7.035 X 106 in STANDARD FORM The exponent is a 6 and it is positive Move the decimal 6 places to the RIGHT 7.035000. 6 places 7,035,000 • Study the exponent • Move the decimal point the Correct number of places to the right • Add any necessary zeros at the END of the number as place holders • Write the number in standard form http://www.youtube.com/watch?v=8bUvkPYXjco LETS PRACTICE SCIENTIFIC NOTATION 5.3 x 104 9.24 x 108 1.205 x 105 DECIMAL MOVEMENT STANDARD FORM EXAMPLE: WITH A NEGATIVE EXPONENT Write 4.16 x 10-5 In STANDARD FORM The exponent is a -5 and it is negative Move the decimal 5 places to the LEFT 0.00004.16. 5 places 0.0000416 • Study the exponent • Move the decimal point the correct number of places to the left • Add any necessary zeros at the BEGINNING to fill up to the decimal point • Write the number in standard form http://www.youtube.com/watch?v=8bUvkPYXjco LETS PRACTICE SCIENTIFIC NOTATION 7.1 x 10-4 5.704 x 10-6 8.65 x 10-2 DECIMAL MOVEMENT STANDARD FORM EXIT TICKET Suppose the table below displays data for the Top prime-time television shows for a given week the year. Complete the empty columns in table by converting the number of households into either scientific notation OR standard form. NAME OF SHOW The Voice NUMBER OF HOUSEHOLDS STANDARD FORM 15,553,000 Duck Dynasty The Simpsons NUMBER OF HOUSEHOLDS SCIENTIFIC NOTATION 1.4623 x 107 0.0865 HOMEWORK • SCIENTIFIC NOTATION PUZZLE http://www.youtube.com/watch?v=QarMTT5YweQ&list=PL698BE8091CA9C622