Presentation on theme: "MATH for SCIENCE Scientific Notation"— Presentation transcript:
1MATH for SCIENCE Scientific Notation Scientists ~A. Deal with:Some very large numbersSome extremely small numbersThese numbers can be quite cumbersome to work with. Tomake it easier scientists frequently use “Scientific Notation.”B. Scientific Notation:A numerical shorthand frequently used for writing very large and extremely small numbers.C. Converting Decimal format to Scientific Notation format:Scientific Notation sets up numbers with:a. Only the leading, non-zero digit/number to the left of the decimal pointin the units place.b. All the remaining numbers are placed to the right of the decimal point.c. Then, that number is multiplied by 10n.
2d. The power/exponent “n” will correspond to: 1. the number of places.2. the direction the decimal point was moved.e. The power “n” is:1. positive (+) when the original number is greater than 12. negative (-) when the original number is less than 1.f. For numbers greater than 1:1. count the number of places the decimal point wasmoved to the left until you have only one non-zeronumber/digit to the left of the decimal point.2. that number becomes the power/exponent that goes tothe upper right of the 10n.
3g. Examples:# Moving the Decimal Pt. Answeri x 104ii x 1022 1iii x 1033 2 1
4h. For numbers less than 1: i. count the number of places the decimal point was moved to the right until you have only one non-zero number/digit to the left of the decimal point.ii. count the number of places the decimal point was moved to the right until you have only one non-zero number/digit to the left of the decimal point.iii. Examples:# Moving the Decimal Pt. Answerx 10 -4x 10 -8x 10 -21 2
5D. Converting Scientific Notation format to Decimal format: 1. For numbers with 10+n :a. Move the decimal point to the right to make the number bigger (greater than 1).b. When you move the decimal point and there are nonumbers left, fill the counting loops in with zeros.Examples:# Moving the Decimal Pt. Answer7.43 x ,000.2.153 x1 26.8 x ,000.
6# Moving the Decimal Pt. Answer 3. For numbers with 10-n :Move the decimal point to the left tomake the number smaller (less than 1).4. Examples:# Moving the Decimal Pt. Answer3.75 x2 18.4 x1.26 x3 2 1
7a. Step 1: Multiply the two leading numbers together. II Computations with Scientific Notation ~ When multiplying or dividing with two or more numbers in Scientific Notation format, the process is done in two stages.A. Multiplication:1. Stage 1 has 2 steps:a. Step 1: Multiply the two leading numbers together.b. Step 2: Multiply the base numbers together.(Remember, this means you just add the powers/exponents.)c. Example:(2.5 x 103) (5.0 x 102)(2.5 x 5.0) (103 x 102)12.5 x 105
82. Stage 2 has 2 steps:These two steps are determined by which format, decimal or ScientificNotation, is required for the answer.Decimal Format Scientific Notation FormatStep 3: Move the decimal point the number Step 3: Take the decimally formatted firstof places and the direction indicated number and change it toby the x 10n exponent Scientific Notation.Step 4: Fill in the blank loops/spaces with Step 4: Multiply the number from step 3zeros. with the base 10 number from step12.5 x x 105(1.25 x 101) (105)1,250, x 106
9B. Examples: 1. (3.3 x 10 -2) (4.5 x 105) (3.3 x 4.5) (10 -2 x 105) Decimal Format Scientific Notation Format14.85 x x 103(1.485 x 101) (103)1 2 314, x 1042. (8.2 x 10-3) (3.6 x 10-2)(8.2 x 3.6) (10-3 x 10-2)29.52 x 10-529.52 x x 10-5(2.952 x 101) (10-5)x 10-4
103. (6.95 x 104) (2.3 x 10-7)(6.95 x 2.3) (104 x 10-7)x 10-3Decimal Format Scientific Notation Formatx x 10-3( x 101) (10-3)3 2 1x 10-2
11C. Division: 1. Stage 1 has 2 steps: Step 1: Divide the two leading numbers, thenStep 2: Divide the base 10 numbers(Remember: this means you just subtract the exponents/powers.)2. Stage 2: Convert the result of stage 1 to either or both decimal format &/or Scientific Notation.D Examples:x → x → 80.2 x 10-3 – (-5) = 80.2 x 102 = 8.02 x 103 or 80201.2 xx 105 → x → 1.2 x 103 or 1,2006.0 xx 104 → x → x 107 = (3.048 x 10-1) (107) = x 1066.3 x or ,048,000
12E. Addition & Subtraction: 1. To add or subtract any number in Scientific Notation, each number MUST:a. Be converted back to decimal format.b. Line up the decimal point.c. Then, add or subtract the numbers.F. Examples:x x x 1021.4 xx9.723 x32, x 104x x 102x6.375 xx 103
13x x x 10-2x4.965 x8.6 xx 102x x 10-37.385 x8.126 xx 10-2