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DO NOW Scientific Notation Conversions DO NOW PROBLEMS Convert into standard notation 1. 7.898 x 105 2. 0.4567 x 10-3 Convert into Scientific Notation 1. 956,400 2. 0.0245 ANSWERS TO DO NOW PROBLEMS Convert into standard notation 1. 789,800 2. 0.0004567 Convert into Scientific Notation 1. 9.56 x 105 2. 2.45 x 10-2 OPERATIONS IN SCIENTIFIC NOTATION LESSON 1.8 CRS STANDARD SIN 402: Understand a simple experimental design OBJECTIVES ►Write numbers in standard and scientific notation. ►Perform calculations with numbers in scientific notation. WHAT IS SCIENTIFIC NOTATION? ►A number expressed in the form: -a number that is between 1 and 9 -multiplied by a power of 10 Example: Neptune is 2,800,000,000 miles from the sun. 2.8 10 9 HOW DO YOU WRITE A NUMBER IN SCIENTIFIC NOTATION? Ex: 3,000,000,000,000 . Where is the decimal point? You move the decimal point to the left until the number in front of it is between 1 and 9. . . 3.0 10 3,000,000,000,000 12 HOW DO YOU WRITE A NUMBER IN SCIENTIFIC NOTATION? Ex: 0.000063 You move the decimal point to the right until the number to the left of it is between 1 and 9. 0.000063 6.3 10 5 Notice that the exponent is negative! WRITE IN SCIENTIFIC NOTATION 234,000,000 Your answer: 2.34 x 108 HOW TO CHANGE NUMBERS IN SCIENTIFIC NOTATION TO STANDARD NOTATION. ►First, decide which way you are going to be moving your decimal point. Negative Exponent – move to the left Positive Exponent – move to the right Move the decimal point the number of the exponent. Ex: 6.35 x 104 = 1.82 x 10-5 = 63,500 0.0000182 WRITE IN STANDARD NOTATION ►9.608 x 109 9,608,000,000 ►3.5 x 10-4 0.00035 ►8.3 x 10-2 0.083 ►5.07 x 106 5,070,000 OPERATIONS WITH SCIENTIFIC NOTATION. Adding: •You just add the first numbers •Your exponents must be the same (4 x 104) + (9 x 104) = (4 + 9) x 104 = 13 x 104 Subtracting: •You just subtract the first numbers •Your exponents must be the same (8 x 104) - (2 x 104) = (8 - 2) x 104 = 6 x 104 OPERATIONS WITH SCIENTIFIC NOTATION. Multiplying: •Multiply the first numbers and then the second numbers. •You just add your exponents (7 x 102)(4 x 105) = (7 4)(102 105) = 28 x 107 OPERATIONS WITH SCIENTIFIC NOTATION. Dividing: •Divide the first numbers and then the second numbers. •You subtract your exponents 5 8.4 10 2 10 8 5 8.4 10 5 8 4 . 2 10 8 2 10 4.2 103 Simplify the exponents. EXIT SLIP 1. (7.5 x104) + (8.0 x104) = 2. 3. (9 x 104) – (6 x103) = (6.2 x 104 ) x (5 x 103) = 4. (9 x 104) = (3 x 102)