Slide 1

Scientific Notation Slide 2 Consists of two parts 1. mantissa The full size number that comes before x 10 2. characteristic The exponent that comes after x 10 and is superscript Slide 3 Scientific Notation Example: 3.00 x 10 15 Mantissa Characteristic Slide 4 Scientific Notation To convert a normal number to scientific notation, move the decimal either to the left or right until you have a mantissa which is greater than -10 or less than +10 Slide 5 Scientific Notation If the absolute value of the number is smaller than 1, the characteristic will be negative If the absolute value of the number is larger than 1, the characteristic will be positive Slide 6 Scientific Notation Example: 542 The absolute value of the number is greater than one so the characteristic is positive 542 Moved to the left two spaces 5.42 x 10 2 Slide 7 Scientific Notation Example: -45000000 The absolute value of the number is greater than one so the characteristic is positive -45000000 Moved to the left seven spaces -4.5 x 10 7 Slide 8 Example: 0.0040 The absolute value of the number is less than one so the characteristic is negative 0.0040 Moved to the right three spaces 4.0 x 10 -3 Slide 9 Example: -0.209 The absolute value of the number is less than one so the characteristic is negative -0.209 Moved to the right one space -2.09 x 10 -1 Slide 10 Example : 9.245 The absolute value of the number is between -10 and +10. 9.245 The decimal is not moved. In this case, the characteristic is zero. 9.245 x10 0 Slide 11 Lets Practice Change 47600000 into scientific notation. = 4.76 x 10 7 Slide 12 Lets Practice Change 0.0890 into scientific notation. = 8.90 x 10 -2 Slide 13 Lets Practice Change 50000 into scientific notation. = 5 x 10 4 Slide 14 Lets Practice Change 50000. into scientific notation. = 5.0000 x 10 4 Slide 15 Lets Practice Change 0.000005454 into scientific notation. = 5.454 x 10 -6 Slide 16 Expanding Scientific Notation to Regular notation If the characteristic is positive, move the decimal to the right. If the characteristic is negative, move the decimal to the left. Slide 17 Expanding Scientific Notation to Regular notation Example 6.50 x 10 2 The characteristic tells us to move two places to the right. 650. Slide 18 Expanding Scientific Notation to Regular notation Example 6.50 x 10 -2 The characteristic tells us to move two places to the left. 0.0650 Slide 19 Lets Practice Convert 9.7 x 10 -2 into regular notation. 0.097 Slide 20 Lets Practice Convert 9.7 x 10 2 into regular notation. 970 Slide 21 Lets Practice Convert 5.60 x 10 2 into regular notation. 560. Slide 22 Lets Practice Convert 6.02 x 10 23 into regular notation. 602,000,000,000,000,000,000,000 Isnt scientific notation great? Slide 23 Fixing Incorrect Scientific Notation Fix the mantissa by moving the decimal Add the fixed characteristic to the original characteristic Slide 24 Example 20.4 x 10 6 (incorrect) Moved over one space to the left (+) to correct the mantissa 2.04 x 10 (6+1) 2.04 x 10 7 (correct) Slide 25 Example 200.4 x 10 -6 (incorrect) Moved over two spaces to the left (+) to correct the mantissa 2.004 x 10 (-6+2) 2.004 x 10 -4 (correct) Slide 26 Example 0.00340 x 10 8 (incorrect) Moved over three spaces to the right (-) to correct the mantissa 3.40 x 10 (8 + -3) 3.40 x 10 5 (correct) Slide 27 Example 0.00340 x 10 -8 (incorrect) Moved over three spaces to the right (-) to correct the mantissa 3.40 x 10 (-8 + -3) 3.40 x 10 -11 (correct) Slide 28 Practice Fix the following incorrect number. 0.000579 x 10 11 5.79 x 10 (-4 + 11) 5.79 x 10 7 (correct) Slide 29 Practice Fix the following incorrect number. 0.040 x 10 -4 4.0 x 10 (-2 + -4) 4.0 x 10 -6 (correct) Slide 30 Practice Fix the following incorrect number. 770.040 x 10 -9 7.70040 x 10 (2 + -9) 7.70040 x 10 -7 (correct) Slide 31 Practice Fix the following incorrect number. 65070.0 x 10 3 6.50700 x 10 (4 + 3) 6.50700 x 10 7 (correct)