Significant Figures

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

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

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

Significant zeros If 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

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

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.)

Example: 42.253 mL 125.6 mL 1.75 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

Example: 62 cm x 33.03 cm = 2047.86 cm2 *only good to 2 figs Multiplication and division Your 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

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.

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

= 4.385 g Example: 4.383 g 0.0023 g 4.3853 g 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

= 8.8105727 = 8.81 oz Example: 250.0 g 1.00 lb 16 oz 454 g 1.00 lb 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

Example: = 2.54 x 10-7 = 2.5 x 10-7 mm/molecule 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

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

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

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

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 Can NOT have accuracy without precision. Can have precision without accuracy