Math for Chemistry Cheat Sheet

Scientific Notation Significant Figures

Metric System (SI): Definitions: How to study chem: Calculator Tips:

Scientific Notation What: a short hand method of writing numbers using the powers of 10 (exponents) *Positive exponents = BIG *Negative exponents = small Converting into sci. not.: Move decimal point after 1st non-zero # Count the number of times the decimal is moved & use this as the exponent Examples: 1027500.456 = 1.027500456 x 106 0.0007543 = 7.543 x 10-4 Converting out of sci. not.: Move the decimal point the number of time of the exponent Examples: 3.25 x 10-5 = 0.0000325 7.2004 x 104 = 72004 *If there is no decimal point, put it at the end  72 = 72. Calculations with sci. not.: Adding/Subtracting: Convert to same exponents Add or subtract numbers & keep exponents Examples: (2.1 x 103) + (3.2 x 103) = (5.3 x 103) (3.5 x 102) – (4.0 x 101) (.40 x 102) = (3.1 x 102) Multiplying: Multiply numbers & add exponents Example: (2 x 106) x (3 x 103) = (6 x 109) Dividing: Divide numbers & subtract exponents Example: (4.2 x 107) ÷ (2.1 x 102) = (2 x 105)

Significant Figures Why: in every measurement there are digits that are known & a digit that is estimated or uncertain What: the digits of a number presented to show accuracy and precision of that measurement Counting: If a decimal is in the number , start with the first non-zero number & count all digits until the end Examples: 10.021  5 sig figs 0.003  1 sig f. If no decimal, start with the first non-zero number & count until the last non-zero number Examples: 202 & 10200  both 3 sig figs Rounding: < 5 then round down & ≥5 then round up Examples: round 6.632 to 3 sig figs  6.63 round 3.4665 to 3 sig figs  3.47 Calculating answers to correct sig figs.: Adding or Subtracting: Determine the least # of decimal places in problem & round to that number of decimal places Example: 10.027 g + 1.5 g = 8.527 g 3 dec 1 dec 8.5 g places place Multiplying or Dividing: Determine the least # of sig figs in problem & round to that # of sig figs Example: 10.027g ÷ 1.50 mL = 6.6847 g/mL 5 sig f 3 sig fig 6.68 g/mL

Metric System (SI): (bu = base unit = gram, liter, or meter) kilo- k x 1000 or centi- c x 0.01 or milli- m x 0.001 or micro- μ x 0.000001 or Examples: 1.25 mL  L 1.25mL x = 0.00125 L 87.5 kg  g 87.5 kg x = 87500 g 0.05 m  μm 0.05 m x = 50000 μm *Don’t forget the unit! *Does it make sense? 1000 bu 1 k 1 bu 100 c 1 bu 1000 m 1 bu 1000000 μ 1 L 1000 mL 1000 g 1 kg 1000000 μm 1 m

Definitions: Accuracy Atom Precision Chemical bond Quantitative Homogeneous Qualitative Heterogeneous IV DV Controlled variable Theory Law Physical change Chemical change Discrete Continuous Line graph Bar graph Mixture Solution Element Compound

How to study chem: -Learn vocabulary (with examples) so you know the word when its used in a question -Look for similarities in problems & use the same steps -Break down problems into steps – identify what you are given & what you need to solve -Keep up with the work

Calculator Tips: -Exponents can look like: 00 EXP EE -Use parentheses when typing in sci not or fractions -Use ÷ for dividing fractions -Use +/- for negative numbers (not the subtract button)