1. Significant Figures

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

3. Rule #2 Zeroes between non-zero digits are significant 2008 has _____ sig figs 108 has _____ sig figs 50000000001 has ____ sig figs

4. Rule #3 Trailing zeroes (those at the end) are not significant unless the number contains a decimal point 90000 has 1 sig fig 900.00 has 5 sig figs 120000 has ____ sig figs 500.00 has ____ sig figs

5. How is it possible to measure 900.00? 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.

6. Rule #4 Zeroes to the left of the first non- zero number are not significant…they are only placeholders 0.00000485 has ____ sig figs 0.052 has ____ sig figs

7. How many sig figs are in the following numbers? 1.0.0004035 ______ 2.100276 ______ 3.2000 ______ 4.150.40 ______ 5.1.980 ______

8. 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

9. Which is least precise? 2.34 + + 10.998 Step 1: Determine least precise number So the answer will have 1 digit beyond the decimal point 4.5

10. Step 2: Do the math 2.34 + 4.5 + 10.998= 17.838

11. Step 3: Round to the appropriate number of sig figs 17.838  17.8 If 5 or greater  round up

12. Try these… 1.17.898 – 15.2 = 2.32 + 19.4 = 3.11.1 + 14.29 -3.33 =

13. 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

14. Which has the fewest number of sig figs? 23.1 x 18.79 = Step 1: determine least precise number So the answer will have 3 digits

15. Step 2: do the math 23.1 x 18.79 = 434.049

16. Step 3: Round to the appropriate number of sig figs 434.049  434

17. Try these… 1.111 5 = 2.12.57 x 3.2 = 3.2.2 x 4.59 x 12.39 =

18. Combined Problems First apply addition/subtraction rules and then apply multiplication/division (4.32 +5.0) x 768 =

19. 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 1.000 cm. What do you think?

20. 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.

21. 35.0 mL – 30.0 mL = 5.0 mL D = m/v D = 18.9 g / 5.0 mL =3.8 g/mL