Chemistry Math Skills

Scientific Notation In Chemistry, you will see VERY LARGE numbers: 120,000,000,000,000,000,000 and VERY SMALL numbers: 0.0000472

Scientific Notation 9.3 x 107 miles 1.24 x 10-5 km Scientific Notation Examples: 6.5 X 106 5.43 X 10-4 (Only list ONE number in front of decimal) Scientific Notation 93,000,000 miles = 0.0000124 km = 9.3 x 107 miles 1.24 x 10-5 km (negative exponent if the number is less than one!)

Express Each in Scientific Notation: 0.135 12,500 3,500,000. 0.0306 0.0000072 1430 1.35 X 10-1 1.25 X 104 3.500000 X106 3.06 X 10-2 7.2 X 10-6 1.430 X 103

Measurements and Sig Figs   Valid Measurements 0 cm 10 Ruler 1 3 cm 2 cm Ruler 2 3.2 cm 3.1 cm 3.3 cm Ruler 3 3.21 cm 3.19 cm 3.20 cm Model 4

How to determine which numbers are “Significant Digits” (SIG FIGS)

Rules for Counting Sig Figs - Details Nonzero integers always count as significant figures. 3,456 m has 4 sig figs. © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Rules for Counting Significant Figures - Details Zeros - Leading zeros do not count as significant figures. 0.0486 mL has 3 sig figs. © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Rules for Counting Sig Figs - Details Zeros - Captive zeros always count as significant figures. 16.07 atm has 4 sig figs. © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Rules for Counting Sig Figs - Details Zeros Trailing zeros are significant only if the number contains a decimal point. 9.300 km 4 sig figs. 9,300 m 2 sig figs. 0.320 L 3 sig figs. 20 kPa 1 sig fig. © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Measurements and Sig Figs   Valid Measurements 0 cm 10 Ruler 1 3 cm 2 cm Ruler 2 3.2 cm 3.1 cm 3.3 cm Ruler 3 3.21 cm 3.19 cm 3.20 cm Model 4

Sig Fig Practice #1 17.10 kg  4 sig figs 100,890 L  5 sig figs How many significant figures in each of the following? 17.10 kg  4 sig figs 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000 mi  2 sig figs © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Get more Sig Fig review ONLINE  Khan Academy is great online tutor! Video – Sig Figs

Calculations and Sig Figs There are guidelines for ROUNDING OFF your answer with the correct number of SigFigs

Calculations and Sig Figs Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation. 6.38 x 2.0 = 12.76 (calculator)  13 (answer) (2 sig figs) Video review

Sig Fig Practice #2 Calculation Calculator says: Answer 3.24 m x 7.0 m 100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3 0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s 1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft 1.030 g ÷ 2.87 mL 0.3588850 g/mL 0.359 g/mL © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Calculations and Sig Figs Addition and Subtraction: Your answer must be rounded off based on the number of decimal places in the least precise measurement. 6.8 cm + 11.934 cm 18.734 cm (calculator) 18.7 (answer) Video review © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Sig Fig Practice #3 Calculation Calculator says: Answer 3.24 m + 7.0 m 100.0 g - 23.73 g 76.27 g 76.3 g 0.02 cm + 2.371 cm 2.391 cm 2.39 cm 713.1 L - 3.872 L 709.228 L 709.2 L 1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb 2.030 mL - 1.870 mL 0.16 mL 0.160 mL © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Helpful Tip for Sig Figs Know your rules! Exact numbers have an infinite number of significant figures. (Important when doing conversions) 1 inch = 2.54 cm, exactly © Chemistry Collaborative edited from Allan @ Sciencegeek.net

Is this you?

Have no fear! ALL formulas you will use this year will ALWAYS be given to you on a reference sheet.

Using Formulas You will only have to ISOLATE a variable. example: D = m/V m = ? V = ? Khan Academy is great online tutor! Video – Rearranging formula to Isolate aVariable

Density   Problem 1 A sample of aluminum is placed in a 25-mL graduated cylinder containing 10.5 mL of water. The level of the water rises to 13.5 mL. Density of Al is 2.7 g/cm3 What is the mass of the aluminum sample?

Density   Problem 2 A metal cube has a mass of 20.0 g and a volume of 5.2 cm3. Is the cube made of pure aluminum? Explain your answer.

Time for Density Lab!

With a partner, choose a small solid object (shell, pebble, bolt, etc) First, pair share: how do we determine the volume of a solid object? Keeping in mind that density = mass divided by volume (D = M/V), write out the steps needed for determining your object’s mass, volume, and density. Write the calculations to determine your object’s density on a separate sheet of paper. Trade your “steps” list and object with another pair and see if you get the same density. Determine the percent error of your results: Step 1: Calculate the error (subtract one value from the other) ignore any negative sign. Step 2: Divide the error by the exact value (we get a decimal number) Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)