# Objectives: (1) To write a number in scientific notation. (2) To perform calculations with numbers written in scientific notation.

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Objectives: (1) To write a number in scientific notation. (2) To perform calculations with numbers written in scientific notation.

Scientific Notation A less confusing way of expressing very large or small numbers Example: 325,000,000,000,000 = 3.25 x 10 14 0.00000000086 = 8.6 x 10 -10

How to convert to scientific notation 1.Convert to a number between 1 and 10 by moving the decimal point left or right. Examples: 45,000 = 4.5 0.00045 = 4.5

2. Write the number from step 1 followed by “x 10.” Examples: 45,000 = 4.5 x 10 0.00045 = 4.5 x 10

Number greater than one = positive exponent Number less than one = negative exponent 3. Write the number of spaces you moved the decimal point as an exponent. Examples: 45,000 = 4.5 x 10 4 0.00045 = 4.5 x 10 -4 Greater than 1 Less than 1

Practice 1.) 3,000 5.) 0.0000000000000002348 2.) 0.0000456 6.) 1,000 3.) 0.004837 7.) 0.000932 4.) 5,800,000 8.) 183,900,000,000

Answers 1.) 3 x 10 3 2.) 4.56 x 10 -5 3.) 4.837 x 10 -3 4.) 5.8 x 10 6 5.) 2.348 x 10 -16 6.) 1.0 x 10 3 7.) 9.32 x 10 -4 8.) 1.839 x 10 11

Going Backwards… Positive Exponent = move the decimal right Negative Exponent = move the decimal left

Practice 1.) 6.023 x 10 5 2.) 9.9 x 10 -4 3.) 2.1 x 10 7 4.) 5 x 10 8 5.) 9.00045 x 10 -5 6.) 9.44 x 10 9 7.) 1.2903 x 10 -1 8.) 3.01 x 10 3

Answers 1.) 6.023 x 10 5 = 602,300 2.) 9.9 x 10 -4 = 0.00099 3.) 2.1 x 10 7 = 21,000,000 4.) 5 x 10 8 = 500,000,000 5.) 9.00045 x 10 -5 = 0.0000900045 6.) 9.44 x 10 9 = 9,440,000,000 7.) 1.2903 x 10 -1 = 0.12903 8.) 3.01 x 10 3 = 3,010

2.5 x 5.0 = 12.5 17 + 14 = 31 Answer = 12.5 x 10 31  1.25 x 10 32

Practice

2.5 / 5.0 = 0.5 17 – 14 = 3 Answer: 0.5 x 10 3  5.0 x 10 2

Practice

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