Calculating with Significant Figures When we do math with these numbers, always round to the number of significant figures represented by the most uncertain number. There are rules, depending on the operations you perform.

Calculating with Significant Figures: Multiplication & Division To determine the number of significant figures in your answer, look for the term with the smallest number of significant figures, because that is the least accurate measurement:

Multiplication Example: 4.56 has three significant figures and 1.4 has two significant figures, therefore round off to two significant figures in your answer = 6.4

Division Example: Example: 8.315 = 0.0279027 Since 298 has the 298 least number of significant figures (3), we round the answer to 0.0279

Multiplication & Division Practice 67.90 ÷ 2 5600 ÷0.368 884.00÷76. 0.0082 ÷ 1.6115 14 x 0.8725 2,096 x 1.3 47,249 x 0.0035 38,000 x 2.72046 536 x 0.000012

Calculating with Significant Figures: Addition & Subtraction To determine the number of significant figures in your answer, find the term with the smallest number of decimal places. Use that many decimal places for your significant figures in your answer.

Addition Example: Example: 12.11 18.0 Since 18.0 has just one + 1.013 decimal place, we will 31.123 round off the answer to one decimal place. = 31.1

Addition & Subtraction Practice 78.50 +6.2106 142.0917 – 3 , 400. – 1.43 62.55 143.1 + 0.21060 1.0917 127.00 .716 + 35.7 ,

Rounding Off Once you have determined how many significant figures is in your answer, there are a few rules for rounding off: Round down if the digit to be removed is less than 5. 1.33 rounded to two significant figures becomes 1.3 Round up if the digit to be removed is 5 or greater. Rounding to two significant figures, 1.36 becomes 1.4 and 3.15 becomes 3.2. If you are removing a string of numbers, only look at the first number to the right. Rounding 4.348 to two significant figures becomes 4.3. In a series of calculations, keep the extra digits until your final result, then round.

Scientific Notation The mass of a proton = 1.67 x 10-27 grams What does this mean???

Review: What are the following #s? 101 102 103 104 100 =10 =10x10=100 =10x10x10=1,000 = 10,000 = 1 10-1 10-2 10-3 10-4 = .1 = .01 = .001 = .0001

Scientific Notation uses a number multiplied by a power of ten: 2000 = 2x103 0.004 = 4x10-3

Rules for Scientific Notation: Add decimal point if it is missing: 3200. Move decimal point so there is ONE non-zero number to the left of it: 3.200 Exponent is the number of places the decimal point was shifted: 3.200x103 Exponent can be positive or negative: 0.0063 = 6.3x10-3

Express in Scientific Notation 4001 32,560,000 78,941,000,000 0.00072 0.00000649 0.00041961