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 2. characteristic 1. mantissa The full size number that comes before x 10 2. characteristic The exponent that comes after x 10 and is superscript

Mantissa Characteristic Scientific Notation Example: 3.00 x 1015 Mantissa 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

Moved to the left two spaces Scientific Notation Example: 542 The absolute value of the number is greater than one so the characteristic is positive Moved to the left two spaces 5.42 x 102

Moved to the left seven spaces Scientific Notation Example: -45000000 The absolute value of the number is greater than one so the characteristic is positive Moved to the left seven spaces -4.5 x 107

Moved to the right three spaces Example: 0.0040 The absolute value of the number is less than one so the characteristic is negative Moved to the right three spaces 4.0 x 10-3

Moved to the right one space Example: -0.209 The absolute value of the number is less than one so the characteristic is negative Moved to the right one space -2.09 x 10-1

Example: 9.245 The absolute value of the number is between -10 and +10. The decimal is not moved. In this case, the characteristic is zero. 9.245 x100

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

Moved over one space to the left (+) to correct the mantissa 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)

Moved over two spaces to the left (+) to correct the mantissa 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)

Moved over three spaces to the right (-) to correct the mantissa 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)

Moved over three spaces to the right (-) to correct the mantissa 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.