Dimensional Analysis

SI Units- System International d’Unites Quantity Symbol Base Unit Abbrev. Length l meter m Mass m kilogram kg Time t second s Temp T kelvin K Amount n mole mol

Volume Units Volume: a liquids volume is found in a graduated cylinder but a solid is found by calculating LxWxH therefore: 1ml =1cm3 1 cm x 1 cm x 1 cm = 1 cubic centimeter

Must Memorize!!! 1000 base unit = 1 kilo- (Ex: 1 km = 1000 m) 1 base unit = 1000 milli- (Ex: 1 m = 1000 mm) 1 base unit = 100 centi- (Ex: 1 m = 100 cm)

Number vs. Quantity UNITS MATTER!! Quantity - number + unit In Science a number without a unit is WORTHLESS! UNITS MATTER!!

Accuracy vs. Precision ACCURATE = CORRECT PRECISE = CONSISTENT Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

Dimensional Analysis-”Bridge” The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out

Dimensional Analysis Steps: 1. Identify given & unknown (starting & ending units) 2. Line up conversion factors so units cancel. 3. Multiply all top numbers then multiply all bottom numbers and then divide. 4. Check units & answer.

Conversion Factors Conversion factors are equivalences of measurements just in different units Example: 1 mile = 5,280 ft Conversion factors can be put into fraction form which is equal to one no matter which is on top and which is on bottom

Lets try one…. 2.8 yrs. to hours ____ years to seconds

Practice 500 m  miles

Numbers in Science Exact numbers are numbers known to be absolutely correct and are obtained by counting or by definition. (Used in math class) Measured numbers involve some estimation. Significant digits are believed to be correct by the person making and recording the measurement.

Significant Figures 2.35 cm Indicate precision of a measurement. Recording Sig Figs Sig figs in a measurement include the known digits plus a final estimated digit You can only be as precise as the instrument you are using!!!! 2.35 cm

Rules for Significant Figures Non-zero digits and zeros between non-zero digits are always significant Leading zeros are not significant Zeros to the right of all non-zero digits are only significant if a decimal point is shown For values written in scientific notation the digits in the coefficient are significant

Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 2. 402 2. 402 3 sig figs 3. 5,280 3. 5,280 3 sig figs 4. 0.080 4. 0.080 2 sig figs

Trick for Significant Figures

Practice Significant Figures 3.0005 L 18.6 mL 2,000 km 18, 345, 600 mm

Sample Problems How many Significant figures are in the following measurements? 3.57 ml 2880 ml 280. ml 24.05 g 3.20 x 104 kg

Scientific Notation 65,000 kg  6.5 × 104 kg Converting into Sci. Notation: Move decimal until there’s 1 digit to its left. Places moved = exponent. Large # (>1)  positive exponent Small # (<1)  negative exponent Only include sig figs.

Practice Problems 2.4  106 g 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm 2.56  10-3 kg 0.00007 km 62,000 mm

Scientific Notation Type on your calculator: = 671.6049383 = 670 g/mol Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your calculator: EXP EE EXP EE ENTER EXE 5.44 7 8.1 ÷ 4 = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

B. Percent Error your value accepted value Indicates accuracy of a measurement your value accepted value

Percent Error % error = 2.9 % A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL. % error = 2.9 %