Scientific notation is a way of expressing really big numbers or really small numbers. Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the analysis must be very precise. It is most often used in “scientific” calculations where the analysis must be very precise. For very large and very small numbers, scientific notation is more concise. For very large and very small numbers, scientific notation is more concise.

MOLES: 1 (one) Mole of any element contains pieces In a practical example if you had 1 mole of M & M’s you would have M & M’s

The particles (atoms) that make up an element are so small they will always be in large numbers – THEREFORE you MUST put numbers in scientific notation to be able to work with them

Positive Exponent: 2.35 x 10 8 Negative Exponent: 3.97 x 10 -7

A number between 1 and 10 A number between 1 and 10 A power of 10 A power of 10 N x 10 x

1) First, move the decimal after the first whole number: ) Second, add your multiplication sign and your base (10) x 10 3) Count how many spaces the decimal moved and this is the exponent x 10

4) See if the original number is greater than or less than one. If the number is greater than one, the exponent will be positive = x 10 5 If the number is less than one, the exponent will be negative = 6.72 x 10 -8

Given: 289,800,000 Given: 289,800,000 Use: (moved 8 places) Use: (moved 8 places) Answer: x 10 8 Answer: x 10 8 Given: Given: Use: 5.67 (moved 4 places) Use: 5.67 (moved 4 places) Answer: 5.67 x Answer: 5.67 x 10 -4

Simply move the decimal point to the right for positive exponent 10. Simply move the decimal point to the right for positive exponent 10. Move the decimal point to the left for negative exponent 10. Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

Given: x 10 6 Given: x 10 6 Answer: 5,093,000 (moved 6 places to the right) Answer: 5,093,000 (moved 6 places to the right) Given: x Given: x Answer: (moved 4 places to the left) Answer: (moved 4 places to the left)

Express these numbers in Scientific Notation: Express these numbers in Scientific Notation: 1) ) ) ) 2 5)

Type You must include parentheses if you don’t use those buttons!! (4.5 x 10 -5) (1.6 x 10 -2) Write in scientific notation x 10 -3

6.E -11 The answer in scientific notation is 6 x The answer in decimal notation is

1386. The answer in decimal notation is 1386 The answer in scientific notation is x 10 3

Left Add – if you move the decimal to the left you add to the exponent If you move the decimal right you - ??????

Adding & Subtracting Adding & Subtracting Rule #1 – the exponents must be the same Rule #1 – the exponents must be the same Examples: Examples: 3.5 x x 10 3 = 6 x x x 10 3 = 6 x x x = 1.3 x x x = 1.3 x 10 10

Rule – If not in scientific notation you must change the exponents Rule – If not in scientific notation you must change the exponents Examples: Examples: 3.5 x x 10 3 = 3.5 x x 10 3 = (350 x x 10 3 = x 10 3 ) put in correct scientific notation – x x x 10 8 = 5.8 x x 10 8 = (5.8 x x = x 10 10)

Multiplying and Dividing Multiplying and Dividing Rule– if multiplying, add the exponents if dividing, subtract the exponents if dividing, subtract the exponentsExamples: 2.2 x 10 3 x 1.0 x 10 3 = 2.2 x x 10 4 / 5.6 x 10 3 = x 10 1 ( x 10 0 )

Multiply or Divide: Multiply or Divide: 1) ( x 10 3 ) (2.7 x ) 1) (3.872 x )/(1.55 x 10 3 )