Units of Measure & Conversions

Number vs. Quantity  Quantity - number + unit UNITS MATTER!!

SI Units QuantityBase UnitAbbrev. Length Mass Time Temp meter kilogram second kelvin m kg s K Amountmolemol Symbol l m t T n

SI Units mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor kilo-k10 3 BASE UNIT

SI Prefix Conversions 1.Find the difference between the exponents of the two prefixes. 2.Move the decimal that many places. To the left or right?

= SI Prefix Conversions NUMBER UNIT NUMBER UNIT 532 m = _______ km 0.532

SI Prefix Conversions mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 move left move right BASE UNIT

SI Prefix Conversions 1) 20 cm = ______________ m 2) L = ______________ mL 3) 45  m = ______________ nm 4) 805 dm = ______________ km ,000 32

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

Dimensional Analysis  Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by each bottom number. 4. Check units & answer.

Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm1 in 2.54 cm = 3.2 in cmin

Dimensional Analysis 6) Lake Taylor football needs 550 cm for a 1 st down. How many yards is this? 550 cm 1 in 2.54 cm = 6.0 yd cmyd 1 ft 12 in 1 yd 3 ft

Dimensional Analysis 7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? 1.3 m 100 cm 1 m = 86 pieces cmpieces 1 piece 1.5 cm

Warm-Up: Density  What is the density of an object that has a mass of 8.76 g and a volume of 3.07 cm3?  Find the density of a granite if a rectangular piece, 5.00 cm by 10.0 cm by 23.0 cm, has a mass of 3220 g.  Iron has a density of 7.9 g/mL. What volume would 10.0 g of iron occupy?  Determine the density of an object that has a mass of 50.50g and when placed in a graduated cylinder containing 50.0 mL of water causes the new volume to be 63.2 mL.

 In your book read section 1.3 p22-26  Make notes on the different types of graphs and when we use them  Do practice problem #1-3 on p24

Scientific Notation  Converting into Scientific 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. 65,000 kg  6.5 × 10 4 kg

Scientific Notation 7. 2,400,000  g kg 9.7  km  10 4 mm Practice Problems 2.4  10 6  g 2.56  kg km 62,000 mm

Scientific Notation  Calculating with Scientific Notation (5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = nd EE ÷ ÷ 2nd EE ENTER = = 670 g/mol= 6.7 × 10 2 g/mol Type on your calculator:

Accuracy vs. Precision  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

Percent Error  Indicates accuracy of a measurement your value / actual accepted value / theoretical

Percent Error  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 %

Proportions  Direct Proportion  Inverse Proportion y x y x

Derived Units  Combination of base units.  Volume (m 3 or cm 3 )  length  length  length D = MVMV 1 cm 3 = 1 mL 1 dm 3 = 1 L  Density (kg/m 3 or g/cm 3 )  mass per volume

Density Mass (g) Volume (cm 3 )

Density  An object has a volume of 825 cm 3 and a density of 13.6 g/cm 3. Find its mass. GIVEN: V = 825 cm 3 D = 13.6 g/cm 3 M = ? WORK : M = DV M = (13.6 g/cm 3 )(825cm 3 ) M = 11,200 g

Density  A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK : V = M D V = 25 g 0.87 g/mL V = 29 mL

Significant Figures  Indicate precision of a measurement.  Recording Sig Figs  Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

Significant Figures  Counting Sig Figs (pg. 57)  Count all numbers EXCEPT:  Leading zeros  Trailing zeros without a decimal point -- 2,500

, Significant Figures Counting Sig Fig Examples , sig figs 3 sig figs 2 sig figs

Significant Figures  Calculating with Sig Figs  Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = g 324 g 4 SF3 SF

Significant Figures  Calculating with Sig Figs (con’t)  Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer mL mL 7.85 mL 224 g g 354 g  7.9 mL 3.75 mL mL 7.85 mL Since no decimals, the number stays as is

Significant Figures  Calculating with Sig Figs (con’t)  Exact Numbers do not limit the # of sig figs in the answer.  Counting numbers: 12 students  Exact conversions: 1 m = 100 cm  “1” in any conversion: 1 in = 2.54 cm

Significant Figures 5. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL  18.1 g g g g 4 SF2 SF  2.4 g/mL 2 SF