Significant Figures and Percent Error

Rules for Significant Figures Nonzero numbers are ALWAYS significant. 1287 g 78,483 cm 58 mL 638 mol = 4 Sig Figs = 5 Sig Figs = 2 Sig Figs = 3 Sig Figs

Rules for Significant Figures Zeros in-between nonzero numbers are ALL significant. 101 mol 20,375 cd 1001 J 908 s = 3 Sig Figs = 5 Sig Figs = 4 Sig Figs = 3 Sig Figs

Rules for Significant Figures Zeros after nonzero numbers (trailing zeros) WITH A DECIMAL PRESENT are significant 6.0 mg 678.10 Kg 80.0 m 12.00 mL = 2 Sig Figs = 5 Sig Figs = 3 Sig Figs = 4 Sig Figs

Rules for Significant Figures Zeros in front of nonzero digits (preceding zeros) are not significant. They are called place holders. 0.78 Kg 0.0309 cd 290 amp 300 s = 2 Sig Figs = 3 Sig Figs = 2 Sig Figs = 1 Sig Figs

Zeros that are significant. = 3 Sig Figs 202 cm 510002 L 144.0 kg 670.00 cd = 6 Sig Figs = 4 Sig Figs = 5 Sig Figs

Zeros that are NOT significant, PLACE HOLDERS. = 1 Sig Figs 50 g 0.0072 m 0.0321 J 9000 L = 2 Sig Figs = 3 Sig Figs = 1 Sig Figs

= 4 Sig Figs = 3 Sig Figs = 4 Sig Figs = 4 Sig Figs Zeros that are significant (called Trailing) and zeros that are not significant (call Place Holder). = 4 Sig Figs 80020 s 0.00401 kg 0.03020 Amp 10230 L = 3 Sig Figs = 4 Sig Figs = 4 Sig Figs

Making Calculations with Significant Digits Multiplying and Dividing The final answer is rounded to have the same number of significant figures as the measurement with the least number of significant figures. 755 cm x 33 cm = 24915 92 m x 20 m = 1840 25000 cm2 2000 m2

0.894 g / 2.0 g = 0.447 g 40.0 x 3.8 = 152 203 x 4589 = 931567 10259 / 789 = 13.00253485 96.0 / 75.0 = 1.25 101 x 0.020 = 2.02 0.45g 1.50 932000 13.0 1.25 2.0

Making Calculations with Significant Digits Adding and Subtracting The final answer is rounded so that it has the same number of digits past the decimal as the measurement with the least number of digits past the decimal 120.60 89.001 6.3 215.901 + 215.9

756.05 23.02 733.03 − 733.03 9.002 2.32 45.659 56.981 + 56.98

45 32.5 12.5 − 13

|Approximate Value − Exact Value| PERCENT ERROR   |Approximate Value − Exact Value|   × 100% |Exact Value| Step 1: Calculate the error (subtract one value form the other) ignore any minus sign. Step 2: Divide the error by the exact value (you will get a decimal number) Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

GOOD MORNING!!  PICK UP: Calculator GET OUT: Notebook, pencil, TURN IN: Pennies if you brought them!! ‘ WARM UP: 1. How many significant figures are in these numbers? a. 803800 b. 803800.0 c. 0000000.3 d. .0000021 e. 84 2. In your own words, what is the definition of accuracy and precision? 3. In the lab, Sandy and Danny produced 8.5 grams of their product. According to their calculations, they should have produced 9.5 grams. What was their percent error? (about 10%)