Significant Figures

1. Significant Figures

2. Accuracy & Precision Accuracy: how close a measurement is to the true value of the quantity that was measured. Precision: how closely two or more measurements of the same quantity agree with one another

3. More Vocab • Accepted Value – The correct value based on reliable references. For example, water SHOULD boil at 100.0°C. • Experimental Value – the value that you measure in lab.

4. Error and Percent Error • Error = experimental value – accepted value • Percent Error = (|error| / accepted value ) x 100

5. Laboratory measurements are made by reading all digits on the instrument, and estimating one digit.

6. Significant Figures • All the digits of a measurement that you are sure of (markings on the instrument) plus one estimated digit.

7. Rules for significant digits. • Nonzero digits are always significant. • Example: 5.67 • All final zeros used after the decimal point are significant. • Example: 5.60 • Zeros between two other significant digits are always significant. • Example: 5006, 5.006 • Zeros used solely for spacing the decimal point are not significant. • Example: 56,000 , 0.566 , 0.560

8. Significant zerosIf a zero is used only to place the decimal, it is NOT significant. Examples: • Desk measures 32.10 cm • What is the last marking on the instrument? • How many significant figures in this number. • Counting numbers are exact whole numbers. • 30 people in the room • $20.05 dollars in my pocket

9. 3 4 1 6 2 4 You try it! 405 3.208 3000 506.089 0.0045 0.0004007

10. Rules for calculating with significant figures. Addition or subtraction Your final answer may contain no more places after the decimal than your least known quantity. (Round the answer so that it has the same number of decimal places as the measurement having the fewest decimal places.)

11. Example: 42.253 mL 125.6 mL1.75 mL 169.603 mL *Answer can only have as many places to the right of the decimal as that of the known quantity with the least:= 169.6 mL

12. Multiplication and divisionYour final answer may have no more total Significant digits than your known quantity with the least number of significant figures. Example: 62 cm x 33.03 cm = 2047.86 cm2 *only good to 2 figs 2.0 x 10 3 cm2

13. Rules for rounding off Look at digit to the right of digit to be rounded.IF: • Greater than or equal to 5 round up, less than 5 leave.

14. Examples:Round to three significant figures. • 8.7257 = • 125.699 = 3.435555 = • 3.425 = • 3.4253 = 8.73 126 3.44 3.42 3.43

15. Example: • If 4.383 g of oxygen • combine with 0.0023 g of carbon, • what’s the mass of the resulting compound? 4.383 g 0.0023 g 4.3853 g = 4.385 g

16. Example: • What is the mass in ounces • of 250.0 g of bromine? 250.0 g 1.00 lb 16 oz 454 g 1.00 lb = 8.8105727 = 8.81 oz

17. Example: • If a line of 1.0 x 108 water molecules is 1.00 inches long, what is the average diameter, in millimeters of a water molecule? 1.00 inch 2.54 cm 1 m 1000 mm 1.0 x 108 molecules 1 inch 100 cm 1 m = 2.54 x 10-7 = 2.5 x 10-7 mm/molecule

18. You try it! • A student places 28.70 g of iron, • 0.3807 oz of aluminum, and 0.00389 lb of • copper in a beaker that weighs 138 g. • What is the total mass in grams of the • beaker and its contents? 0.3807 oz 1.0 lb 454 g 16 oz 1.0 lb 28.70 g 10.8 g 1.77 g 138 g 179.27 = 179 g = 10.8 gAl 0.00389 lb 454 g 1.00 lb = 1.77 gCu

19. You try it! • A girl needs to reflux a mixture • for 9.85 hours. How long must • the mixture reflux in minutes? 9.85 h 60 min 1 h = 591 min

20. You try it! • A group of chemistry students are instructed to measure a 0.75 m length of magnesium ribbon. How long will each ribbon be in mm? 0.75 m 1000 mm 1 m = 750 mm