2. Significant Figure Rules RulesExamples The following are always significant Non zero digits Zeros between non zero digits Zero to the right of a non zero digit and to the left of a written decimal Finishing zeros to the right of a decimal place 673 has 3 506 has 3 1.009 has 4 57.00 has 4 The following are NEVER significant Zeros to the left of the first non zero digit 0.67 has 2 0.004 has 1 EXCEPTIONS Counting numbers Exact conversion factors 30 days in June 100 cm in 1 m

3. Math in Significant Figures Multiplication and Division –The # of significant figures in the result is the same as the # in the least precise measurement used in the calculation –0.024 x 1244= (two significant figures ) Sample Problem: Find the area of a rectangle 2.1 cm by 3.24 cm. –Solution: Area = 2.1 cm x 3.24 cm = 6.8cm 2

4. Math in Significant Figures Addition and Subtraction –The # of significant figures in the result has the same number of decimal places as the least precise measurement –Round to the least # of decimal places Sample Problem: Add 42.56 g + 39.460 g + 4.1g Solution: 42.56 g 39.460 g 4.1 g Sum = 86.1 g

5. Rules for Rounding In a series of calculations, carry the extra digits through to the final result, then round If the digit to be removed –Is less than 5, the preceding digit stays the same –Is equal to or greater than 5, the preceding digit is increased by 1

6. Scientific Notation

8. Why use Scientific Notation? M x 10 n M is a number between 1 and 10 n is an integer all digits in M are significant –if n = (+)#, then move the decimal to the right 1.0 x 10 5 = 100000 –If n = (-)#, then move the decimal to the left 1.0 x 10 -5 =.00005

9. Sample Problems Express these numbers in decimal notation. 1. 8.32 x 10 -2 _____________ 2. 5.4 x 10 4 ______________ 3. 9.67 x 10 3 _____________ 4. 1.457 x 10 2 _____________ 5. 3.00 x 10 -1 _____________ 6. 2.22 x 10 -6 _____________

10. Reducing to Scientific Notation 1. Move decimal so that M is between 1 and 10 2. Determine n by counting the number of places the decimal point was moved a. Moved to the left, n is positive b. Moved to the right, n is negative

11. Sample Problems 47,000 _____________________ 0.00047 ____________________ 0.4100 _____________________ 421 _______________________ 5630 _______________________

12. Mathematical Problems Addition and subtraction –Operations can only be performed if the exponent on each number is the same Multiplication –M factors are multiplied –Exponents are added Division –M factors are divided –Exponents are subtracted (numerator - denominator)

13. Sample Problems 1. (2.8 x 10 5 ) +(7.53 x 10 5) ________________________ 2. (3.1 x 10 -2 ) (4.380 x 10 3 ) ________________________ 3. (4.20 x 10 2 ) (0.040 x 10 -1 ) ________________________ 4. 3.0 x 10 3 ÷ 1.2 x 10 4 ________________________ 5. 4.95 x 10 6 ÷ 2.33 x 10 -2 ________________________