Scientific Notation

Why use scientific notation: Consider the equation: Find the force between an electron and the Earth when the electron is on the surface of the earth

 with only 1 digit to the left of the decimal point Left - Larger Scientific Notation Writing numbers using powers of ten with only 1 digit to the left of the decimal point 4 35 000 3.5 x 10 -3 0.00467 4.67 x 10 Changing numbers to scientific notation Move the decimal pt. to the left- make the exponent larger for each step Left - Larger Move the decimal pt. to the right- make the exponent smaller for each step  exponent decimal Right - Reduce

Move decimal 4 places to the left to reach 3.5, add 4 to the exponent 35 000 3.5 x 104 Same as 35 000 x 100 Move decimal 4 places to the left to reach 3.5, add 4 to the exponent (Left – Larger) 0.00467 Same as 4.67 x 10-3 0.00467 x 100 Move decimal 3 places to the right, subtract 3 from the exponent (Right Reduce)

To expand a number from scientific notation with a positive exp: reduce the exponent to zero and move the decimal point to the right for each reduction of 1. (Reduce Right) 5.635 x 105 = 5 63 500 If the exp. is negative, increase the exp. to 0, and move the exponent left for each 1 added. 0.000 004 879 4.879 x 10-6 = (Larger – Left)

Numbers should be expressed in proper notation Proper Notation - Only 1 number to the left of the decimal in the coefficient Express the following in proper notation 359.4 x 104 = 3.594 x 10? 3.594 x 106 0.468 x 10-6 =4.68 x 10? 4.68 x 10-7 358 x 105 = ? 3.58 x 107 0.020 x 104 = ? 2.0 x 102 (Left – Larger) (Right Reduce)

Multiplication / Division Rules Mathematical Operations with Scientific Notation Multiplication / Division Rules 1. Multiply the coefficients 2. Add the exponents 3. Place in Proper Notation 1. Divide the coefficients 2. Subtract the exponents 3. Place in Proper Notation 6). 9.0 x 107 3.0 x 10-3 5). 5.0 x 104 x 3.0 x 10-6 add subtract (4 +(-6)) = -2 (7 -(-3)) = 10 15.0 x 10-2 3.0 x 1010 1.5 x 10-1

Keep same exponent Written in proper form Addition and Subtraction Rules with Sci not 1. Make exponents the same, if not already 2. Add or Subtract coefficients 3. Keep the same exponent 4. Change to Proper Notation ( if not already) Examples 1). 5.6 x 105 +8.2 x 105 Exponents are already the same Keep same exponent 13.8 x 105 6 Written in proper form 1.38 x 10

Addition and Subtraction Rules with Sci not 2). 4.5 x 10-3 + 3.4 x 10-4 Need to match exponents 4.5 x 10-3 Keep value with higher exp the same Change lesser valued exp to match higher and adjust coefficient + 0.34 x 10-3 4.84 x 10-3 Already in correct form 4. 6.9 x 105 - 4.8 x 107 3. 6.9 x 105 - 4.8 x 104 0.069 x 107 6.9 x 105 - 4.8 x 107 -0.48 x 105 -4.731 x 107 6.42 x 105