Presentation on theme: "Adding/Subtracting/Multiplying/Dividing Numbers in Scientific Notation"— Presentation transcript:
1 Adding/Subtracting/Multiplying/Dividing Numbers in Scientific Notation
2 How wide is our universe? 210,000,000,000,000,000,000,000 miles(22 zeros)This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.
3 A number is expressed in scientific notation when it is in the form a x 10nwhere a is between 1 and 10and n is an integer
4 An easy way to remember this is: If an exponent is positive, the number gets larger, so move the decimal to the right.If an exponent is negative, the number gets smaller, so move the decimal to the left.
5 When changing from Standard Notation to Scientific Notation: 4) See if the original number is greater than or less than one.If the number is greater than one, the exponent will be positive.= x 105If the number is less than one, the exponent will be negative.= 6.72 x 10-8
6 Write the width of the universe in scientific notation. 210,000,000,000,000,000,000,000 milesWhere is the decimal point now?After the last zero.Where would you put the decimal to make this number be between 1 and 10?Between the 2 and the 1
7 2.10,000,000,000,000,000,000,000.How many decimal places did you move the decimal?23When the original number is more than 1, the exponent is positive.The answer in scientific notation is2.1 x 1023
8 Write 28750.9 in scientific notation. x 10-5x 10-4x 104x 105
9 2) Express 1.8 x 10-4 in decimal notation. 3) Express 4.58 x 106 in decimal notation.4,580,000
10 Try changing these numbers from Scientific Notation to Standard Notation: 9.678 x 104x 10-3x 107x 10-596780
11 Write in PROPER scientific notation Write in PROPER scientific notation. (Notice the number is not between 1 and 10) 8) x 1092.346 x 10119) x 1046.42 x 10 2
12 Adding/Subtracting when Exponents are Equal When the exponents are the same for all the numbers you are working with, add/subtract the base numbers then simply put the given exponent on the 10.
13 General Formulas (N X 10x) + (M X 10x) = (N + M) X 10x (N X 10y) - (M X 10y) = (N-M) X 10y
14 Example 1 Given: 2.56 X 103 + 6.964 X 103 Add: 2.56 + 6.964 = 9.524 Answer: X 103
15 Example 2Given: 9.49 X 105 – X 105Subtract: 9.49 – = 4.627Answer: X 105
16 Adding With the Same Exponent (3.45 x 103) + (6.11 x 103)= 9.569.56 x 103
17 Subtracting With the Same Exponent (8.96 x 107) – (3.41 x 107)8.96 – 3.41 = 5.555.55 x 107
18 Adding/Subtracting when the Exponents are Different
19 When adding or subtracting numbers in scientific notation, the exponents must be the same. If they are different, you must move the decimal either right or left so that they will have the same exponent.
20 Moving the DecimalFor each move of the decimal to the right you have to add -1 to the exponent.For each move of the decimal to the left you have to add +1 to the exponent.
21 Continued…It does not matter which number you decide to move the decimal on, but remember that in the end both numbers have to have the same exponent on the 10.
22 Example 1Given: 2.46 X X 103Shift decimal 3 places to the left for 103.Move: X 103+3Add: 2.46 X X 106Answer: X 106
23 Example 2Given: X 103 – 2.65 X 10-1Shift decimal 4 places to the right for 10-1.Move: X 10(-1+4)Subtract: X X 103Answer: X 103
24 (4.12 x 106) + (3.94 x 104)(412 x 104) + (3.94 x 104)=x 104Express in proper form: 4.15 x 106
25 Subtracting With Different Exponents (4.23 x 103) – (9.56 x 102)(42.3 x 102) – (9.56 x 102)42.3 – 9.56 = 32.7432.74 x 102Express in proper form: 3.27 x 103
26 Multiplying… The general format for multiplying is as follows… (N x 10x)(M x 10y) = (N)(M) x 10x+yFirst multiply the N and M numbers together and express an answer.Secondly multiply the exponential parts together by adding the exponents together.
27 Multiplying…Finally multiply the two results for the final answer.(2.41 x 104)(3.09 x 102)2.41 x 3.09 = 7.454 + 2 = 67.45 x 106
28 7) evaluate (3,600,000,000)(23). The answer in scientific notation is 8.28 x 10 10The answer in decimal notation is82,800,000,000
29 6) evaluate (0.0042)(330,000). The answer in decimal notation is 1386 The answer in scientific notation is1.386 x 103
30 Write (2.8 x 103)(5.1 x 10-7) in scientific notation.
31 Now it’s your turn.Use the link below to practice multiplying numbers in scientific notation.Multiplying in Scientific Notation
32 Dividing… The general format for dividing is as follows… (N x 10x)/(M x 10y) = (N/M) x 10x-yFirst divide the N number by the M number and express as an answer.Secondly divide the exponential parts by subtracting the exponent from the exponent in the upper number.
33 Dividing…Finally divide the two results together to get the final answer.(4.89 x 107)/(2.74 x 104)4.89 / 2.74 = 1.787 – 4 = 31.78 x 103
34 5) evaluate: x x 102 :The answer in scientific notation is6 xThe answer in decimal notation is
35 0.0028125 Write in scientific notation. 2.8125 x 10-3 4) Evaluate: x x 10-2Write in scientific notation.x 10-3
36 Now it’s your turn.Use the link below to practice dividing numbers in scientific notation.Dividing in Scientific Notation
37 Practice Adding and Subtracting in Scientific Notation Practice WorksheetPractice Adding and Subtracting in Scientific NotationAnswers to Worksheet
38 Links for more information and practice Addition and Subtraction with Scientific NotationProblem Solving--Scientific NotationScientific Notation
39 Quiz Time!!!Below is a set of links for a quiz on adding and subtracting numbers in scientific notation, and there is a link to get the answers to the quiz.Adding and Subtracting QuizAnswers to Quiz