- 2. SIGNIFICANT DIGITS Rule #1: All non-zero numbers are significant Ex. 5489.213 7 significant digits
- 3. SIGNIFICANT DIGITS Rule #2: All zeros located between non-zero numbers are significant Ex. 0.08006 4 significant digits
- 4. SIGNIFICANT DIGITS Rule #3: Zeros located to the left of a value are not significant Ex. 0.00004 1 significant digit
- 5. SIGNIFICANT DIGITS Rule #4: Zeros that are located to the right of a value may or may not be significant Ex. 1000.mL 4 significant digits Ex. 1000mL 1 significant digit
- 6. SIGNIFICANT DIGITS Ex. 1000mL 1 significant digit Why? 1000mL could have been anything from 951mL to 1049mL
- 7. SIGNIFICANT DIGITS Ex. 1000.0mL 5 significant digits Why? Rule #5 Any 0’s to the right of a decimal that are not followed by any number are significant
- 8. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #1: Multiplying and Dividing 1.008 x 4.67 = 4.70736 = 4.71 This value has the lowest number of significant digits The value with the lowest number of significant digits determines how many significant digits will appear in the answer
- 9. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #2: Adding and Subtracting 1.008 + 4.67 = 5.678 = 5.68 This value has the lowest number of decimal places The value with the lowest number of decimal places determines how many decimal places will appear in the answer
- 10. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If greater than 5, round up If less than 5, round down
- 11. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round up if the preceding number is odd Ex. 18.35 Odd number 18.4
- 12. CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round down if the preceding number is even Ex. 18.25 Even number 18.2
- 13. CALCULATIONS WITH SIGNIFICANT DIGITS 12cm 6.782cm 5.18cm Calculate the volume of the rectangular prism
- 14. CALCULATIONS WITH SIGNIFICANT DIGITS 12cm 6.782cm 5.18cm V= l x w x h = (5.18cm) x (6.782cm) x (12cm) = 421.56912cm3 = 4.2 x 102 cm3 “12” has the lowest number of significant digits. So the answer must have 2 significant digits.
- 15. SIGNIFICANT DIGITS Practice: How many significant digits are in the following values? a) 5.703 b) 70 c) 100. d) 395830 e) 0.0101 f) 21.0 Practice: Round the following numbers to 2 significant digits a) 1.01 b) 24.5 c) 17.5 d) 25.6 e) 48665 f) 11.5
- 16. SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm
- 17. SIGNIFICANT DIGITS Practice: How many significant digits are in the following values? a) 5.703 4 b) 70 1 c) 100. 3 d) 395830 5 e) 0.0101 3 f) 21.0 3 Practice: Round the following numbers to 2 significant digits a) 1.01 1.0 b) 24.5 24 c) 17.5 18 d) 25.6 26 e) 48665 4.9x104 f) 11.5 12
- 18. SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm = 12.0373cm = 12cm = 1060.20288cm3 = 1.1x103 cm3
- 19. SIGNIFICANT DIGITS Significant digits for logarithmic values: If a solution had an H+ concentration of 2.5x10-4 mol/L, then what is the pH to the correct number of significant digits? i.e. pH = - log [2.5x10-4 mol/L] pH = 3.602059 These two digits are significant This digit is derived from the power of 10, so it is not a significant digit The two digits to the right of the decimal are significant .: pH = 3.60
- 20. SIGNIFICANT DIGITS What is the volume of the graduated cylinder? What digits are you absolutely sure about? 6.6mL, 6.61mL, or 6.62mL? 6.6mL So there are 2 significant digits in your measurement
- 21. SIGNIFICANT DIGITS What is the volume of the graduated cylinder? What digits are you absolutely sure about? 21.5mL or 21.50mL? 21.5mL So there are 3 significant digits in your measurement
- 22. SIGNIFICANT DIGITS If the scale says that your sample is 30.69g, then how many significant digits are in this value? 4 significant digits It is NOT 30.690g, because the scale is not accurate to 3 decimal places You cannot be more accurate than what your instrument allows.