Significant Figures I love teaching Chemistry!

How do you know when to round a number? There are rules to help us know which numbers are significant (important)

Rule #1 All non-zero numbers are significant 284 has ____ sig figs 123,456 has _____ sig figs 3 6

Rule #2 Zeroes between non-zero digits are significant 2008 has _____ sig figs 108 has _____ sig figs has ____ sig figs

Rule #3 Trailing zeroes (those at the end) are not significant unless the number has a decimal point has 1 sig fig has 5 sig figs has ____ sig figs has ____ sig figs 2 5

How is it possible to measure ? The number of decimal places in a measurement depends on what equipment (measurement tool) is used Researchers report all digits they are certain of (sure of) plus one digit they are uncertain of

20.0 mL 28.1 mL

73.1 mL

Rule #4 Zeroes to the left of the first non- zero number are not significant…they are only placeholders (they make the number easier to read) has ____ sig figs has ____ sig figs 2 3

How many sig figs are in the numbers below? ______ ______ ______ ______ ______

Precision vs. Accuracy Precision: reproducibility or repeatibility Accuracy: degree of closeness to an accepted value

Rules for Addition and Subtraction Your calculated value will have the same number of sig figs to the right of the decimal point as that of the least precise quantity

Which is least precise? Step 1: Determine least precise number So the answer will have 1 digit beyond the decimal point 4.5

Step 2: Do the math =

Step 3: Round to the appropriate number of sig figs  17.8 If 5 or greater  round up

Try these… – 15.2 = = =

Rules for Multiplication and Division The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs

Which has the fewest number of sig figs? 23.1 x = Step 1: determine least precise number So the answer will have 3 digits

Step 2: do the math 23.1 x =

Step 3: Round to the appropriate number of sig figs  434

Try these… = x 3.2 = x 4.59 x = 22.2   130

Combined Problems First apply addition/subtraction rules and then apply multiplication/division ( ) x 768 =  7100

Why are sig figs used? The science teachers at a Baltimore County middle school wished to acquire a steel cube, one cubic centimeter in size to use as a visual aid to teach the metric system. The machine shop they contacted sent them a work order with instructions to draw the cube and specify its dimensions. On the work order, the science supervisor drew a cube and specified each side to be cm.

When the machine shop received this job request, they contacted the supervisor to double check that each side was to be one centimeter to four significant figures. The science supervisor, not thinking about the "logistics", verified four significant figures. When the finished cube arrived approximately one month later, it appeared to be a work of art. The sides were mirror smooth and the edges razor sharp.

When they looked at the "bottom line", they were shocked to see the cost of the cube to be $500! Thinking an error was made in billing, they contacted the machine shop to ask if the bill was really $5.00, and not $500. At this time, the machine shop verified that the cube was to be made to four significant figure specifications.

It was explained to the school, that in order to make a cube of such a high degree of certainty, in addition to using an expensive alloy with a low coefficient of expansion, many man hours were needed to make the cube. The cube had to be ground down, and measured with calipers to within a certain tolerance. This process was repeated until three sides of the cube were successfully completed.

So, "parts and labor" to prepare the cube cost $500. The science budget for the school was wiped out for the entire year. This school now has a steel cube worth its weight in gold, because it is a very certain cubic centimeter in size.

Exit Slip Using a triple beam balance and a graduated cylinder, a student collected data on a sample of an element: Mass of sample = 18.9 g Volume of water = 30.0 mL Volume of water and sample = 35.0 mL Calculate the density of the sample using sig figs.

35.0 mL – 30.0 mL = 5.0 mL D = m/v D = 18.9 g / 5.0 mL =3.8 g/mL