Scientific Notation Objectives Express numbers in scientific notation

Scientific Notation

Objectives �Express numbers in scientific notation. �Convert from standard form to scientific notation. �Convert from scientific notation to standard form. �Add, Subtract, Multiply, and Divide with scientific notation.

Scientific Notation Intro

Scientific Notation �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

Scientific Notation �Example: 3. 00 x Mantissa 15 10 Characteristic

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

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

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 102

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 107

�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 -3 10

�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 -1 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 x 100

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.

Expanding Scientific Notation to Regular notation Example 6. 50 x 102 The characteristic tells us to move two places to the right. 650.

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

Fixing Incorrect Scientific Notation �Fix the mantissa by moving the decimal �Add the “fixed” characteristic to the original characteristic

Example 20. 4 x 106 (incorrect) Moved over one space to the left (+) to correct the mantissa 2. 04 x 10(6+1) 2. 04 x 107 (correct)

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)

Example 0. 00340 x 108 (incorrect) Moved over three spaces to the right (-) to correct the mantissa 3. 40 x 10(8 + -3) 3. 40 x 105 (correct)

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)

Adding and Subtracting Scientific Notation �The mantissa MUST have the same characteristic. �Then add or subtract the mantissa. �Finally correct the scientific notation if needed

Multiplying Numbers in Scientific Notation �Multiply the mantissas �ADD the characteristics together �Correct the number if the mantissas are +10 or greater/-10 or less.

Dividing Numbers in Scientific Notation �Divide the mantissas �Subtract the characteristic of the denominator from the characteristic of the numerator �Correct the number if the mantissas are +10 or greater/-10 or less.