Significant Figures

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

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 contains a decimal point has 1 sig fig has 5 sig figs has ____ sig figs has ____ sig figs

How is it possible to measure ? The number of decimal places in a measurement depends on the equipment used. Researchers report all digits they are certain of plus one unit they are uncertain of.

Rule #4 Zeroes to the left of the first non- zero number are not significant…they are only placeholders has ____ sig figs has ____ sig figs

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

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 =

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

Why are sig figs used? The science teachers at Rye High 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. What do you think?

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