Math Tool Kit for Chemistry

Goals and Objectives What is the correct way to take a measurement? What are significant figures in a measurement? How do we count SFs in a measurement? How do we use SFs in a calculation? How do we round off answers correctly? How is scientific notation used? What is a percent error calculation? What units of measurement do scientists use around the world? How do we convert units of measurement?

Reliable Measurements ACCURATE: close to the true value PRECISE: close to each other, repeatable RECORDED CORRECTLY: have one estimated digit When used in calculations they are rounded correctly!

All measurements should have ONE estimated digit between the markings

You Try 

1.36 cm

You Try 

1.25 cm 2.2 cm

You Try 

2.8 2.70 27 27.0

Uncertainty in measurements Different scales and different estimations result in UNCERTAINTY in all measurements.

You Try 

21.5 mL

Measuring Mass Our balances have FOUR beams. They are very precise and require your patience and skill! The last beam is read to 3 decimals.

171.483 g

https://youtu.be/XTHTBvXFZns https://youtu.be/Gw9iDbz84bs

Counting SFs

NEVER SIGNIFICANT ALWAYS SIGNIFICANT Leading zeroes Trailing zeroes IF THERE IS NO DECIMAL IN THE MEASUREMENT Non-zero numbers Captive zeroes Trailing zeroes IF THERE IS A DECIMAL IN THE MEASUREMENT

This measurement has 10 SFs!

You Try  0.003 900 270 7 SFs 9 024 000 4 SFs 9 024 000.0 8 SFs

Significant Figures - You Try  Examples: How many significant figures? 99,000 2 sig figs 99,000. 5 sig figs 0.0099 2 sig figs 0.0990 3 sig figs

Trick for counting SFs

Counting Significant Figures The Atlantic – Pacific Rule: Pacific (Present): If decimal point is present, start with the first non-zero number on the left. Atlantic (Absent): If decimal point is absent, start with the first non-zero number on the right.

You Try  10.2 103 103.0 200 5.68800 5,269,000 00.2006 10.036 0.258 0.00689

You Try  10.2 103 103.0 200 5.68800 5,269,000 00.2006 10.036 0.258 0.00689 3 4 1 6 5

Calculating with Significant Figures (+/-) When you use your measurements in calculations, your answer may only be as exact as your least exact measurement. For addition and subtraction, round to the fewest decimal places. Example: (3 decimals) (1 decimal) (unrounded) (rounded) 50.259 + 17.4 = 67.659 67.7 Example: (3 decimals) (2 decimals) (unrounded) (rounded) 25.294 - 2.54 = 22.354 22.35

Calculating with Significant Figures (+/-) For addition and subtraction, round to the fewest decimal places Watch out for these….. Example: (2 decimals) (2 decimals) (unrounded) (rounded) 10.01 - 1.01 = 9 9.00 Example: (0 decimals) (3 decimals) (unrounded) (rounded) 38 + 63.344 = 101.344 101

Practice Rounding Your Answers Examples: Round each to TWO decimals Br = 79.904 79.90 N = 14.0067 14.01 Kr = 83.798 83.80 Ag = 107.8682 107.87

Calculating with Significant Figures (x/÷) When you use your measurements in calculations, your answer may only be as exact as your least exact measurement. For multiplication and division, round to the fewest significant figures. Example: (5 SFs) (3 SFs) (unrounded) (rounded) 50.259 m x 17.4 m = 874.5066 m2 875 m2 Example: (3 SFs) (1 SF) (unrounded) (rounded) 0.365 m3 ÷ 0.02 m = 18.25 m2 20 m2

Calculating with Significant Figures (x/÷) When you use your measurements in calculations, your answer may only be as exact as your least exact measurement. For multiplication and division, round to the fewest significant figures. Example: (3 sigfigs) (1 sigfig) (unrounded) (rounded) 0.135 x 20 = 2.7 3

Practice Rounding Your Answers Examples: Round each to 3SFs 40.06 40.1 0.17354 0.174 0.2006 0.201 5 269 000 5 270 000

Scientific Notation A shorthand system of writing very large or very small numbers. The power of 10 (the exponent), is the number of times the decimal point is moved. The coefficient must be between 1 and 10.

Scientific Notation - You Try  Examples: What would each of these numbers be in scientific notation? NOTE: Retain the same SFs!!! 3000 3 x 103 32,000 3.2 x 104 0.05 5 x 10-2 0.0058 5.8 x 10-3

Scientific Notation & Significant Figures - You Try  Always retain the same SFs when changing from scientific notation ⟷ standard notation 99,000 2 SFs = 9.9 x 10 4 99,000. 5 SFs = 9.9000 x 10 4 0.0099 2 SFs = 9.9 x 10 -3 0.0990 3 SFs = 9.90 x 10 -2

SFs, Rounding, SN Examples: Round as indicated and answer in SN 99,000 3 SFs & SN 9.90 x 104 0.0099 1 SF & SN 1 x 10-3

Percent Error Calculations % ERROR = |𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝑽𝒂𝒍𝒖𝒆 −𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆| 𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆 x 100 Example: A student measures a mass of 3.697g and the true value is 4.155 g. What is the percent error in the measurement? 𝟑.𝟔𝟗𝟕 −𝟒.𝟏𝟓𝟓 𝟒.𝟏𝟓𝟓 x 100 = 𝟎.𝟒𝟓𝟖 𝟒.𝟏𝟓𝟓 x 100 = 11.0% (3SF) ALWAYS SHOW ALL THREE STEPS IN YOUR WORK!

You Try  % ERROR = |𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒅 𝑽𝒂𝒍𝒖𝒆 −𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆| 𝑻𝒓𝒖𝒆 𝑽𝒂𝒍𝒖𝒆 x 100 What is the % error for a volume measurement of 4.26mL if the accepted value is 4.14mL?

Units of Measurement: 7 Fundamental SI Units Property SI Unit and Standard of Measurement Symbol Length meter m Mass kilogram kg Time second s Temperature Kelvin K Amount of Substance mole mol Current ampere A Luminous Intensity candela cd

Derived Units Property Meaning Derived Unit Symbol Area l x w   Area l x w square meter m2 m x m Volume l x w x h cubic meter m3 m x m x m Volume (liquid) cubic decimeter dm3 dm x dm x dm Force mass x acceleration newton N 1N = 1kg-m/s2 Pressure force/area pascal Pa 1Pa = 1N/m2 Energy force x distance joule J 1J = 1N-m Frequency cycles/second hertz Hz 1Hz = 1wave cycle/second Density mass/volume m/s, km/hr, m/min, etc. Speed distance/time kg/m3, g/cm3, g/mL, etc

SFs, Rounding, SN Examples: How many significant figures? 99,000 2 sig figs 99,000. 5 sig figs 0.0099 2 sig figs 0.0990 3 sig figs

Practice http://studymaths.co.uk Worksheets tab Select numbers Lesson 47, 32,4