Scientific Notation

Scientific Notation Why do we need to know this? It’s hard to work with numbers like this: 6,000,000,000,000,000,000,000 Or this 0.00000000000000000000876 What is scientific notation? Simplifying large or small numbers by converting them to a number between 1 and 10 multiplied by powers of 10

Scientific Notation Powers of 10? 10 x 10 x 10 = 1000 or 103 10-n = 1/10n So 10-3 = 1/103 = 1/1000 = 0.001

Converting Standard notation to Scientific Notation Always move the decimal so there is one number LEFT of the decimal If the original number is LARGER than 1 and the decimal is moved to the LEFT, use a positive exponent 1,567 = 1.567 x 103 If the original number is SMALLER than 1 and the decimal is moved to the RIGHT, use a negative exponent 0.0000045 = 4.5 x 10-6

1. Move the decimal to the right of the first non-zero number. To write a number in scientific notation: 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive.

Converting from scientific notation to Standard notation Move the decimal the number of places indicated by the exponent. If the exponent is positive, your final number should be larger than 1 5.6 x 102 = 560 I f the exponent is negative, your final number should be smaller than 1 5.6 x 10-2 = 0.056

Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105) Multiplication When multiplying numbers written in scientific notation…..multiply the first factors and add the exponents. Sample Problem: Multiply (3.2 x 10-3) (2.1 x 105) Solution: Multiply 3.2 x 2.1. Add the exponents -3 + 5 Answer: 6.7 x 102

Sample Problem: Divide (6.4 x 106) by (1.7 x 102) Division Divide the numerator by the denominator. Subtract the exponent in the denominator from the exponent in the numerator. Sample Problem: Divide (6.4 x 106) by (1.7 x 102) Solution: Divide 6.4 by 1.7. Subtract the exponents 6 - 2 Answer: 3.8 x 104

Adding and Subtracting in Scientific Notation (5.8 x 103) + (2.16 x 104) Step 1 – move the decimal of one so they both have the same power of ten (5.8 x 103) + (21.6 x 103) Step 2 – add or subtract the numbers without their powers of ten exponents 5.8 + 21.6 = 27.4 Step 3 – rewrite with the same power of ten. 27.4 x 103 Step 4 – move the decimal (if needed) to get it back into scientific notation form 2.74 x 104