Measurements and Calculations Scientific Method Units of Measurement Using Scientific Measurements

Types of information Qualitative-non-numerical data The sample of copper is shiny Quantitative-numerical data The sample of copper has a mass of 4.7 grams

Qualitative or quantitative? The liquid floats on water Qualitative The liquid has a temperature of 55.6°C Quantitative The metal is malleable Qualitative

Units of Measurement

Measurements: Number & unit! Measurements represent quantities such as volume or length. Measurements must include a number and unit!

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

SI Prefixes mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 BASE UNIT You must know and be able to convert between these prefixes!!

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 Example 1 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 Example 2 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

Conversions For SI units, you can move the decimal to convert between prefixes. Find the difference in the exponents of the 2 prefixes and move the decimal that many places. If the prefix you’re going to is larger, move the decimal to the left. If the prefix you’re going to is smaller, move the decimal to the right.

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 Conversion Examples 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 Deriving conversion factors: If I know that 1 inch is equal to 2.54 cm, then I can write 2 conversion factors: 1 in = 2.54 cm 2.54 cm 1 in = 2.54 cm 1 in 1 in = 11 = I can use these conversion factors to convert between inches and centimeters.

Dimensional Analysis Ex. 1 How many milliliters are in 1.00 quart of milk? Starting unit: Ending unit: Equalities: 1 qt=1.057 L, 1 L=1000 mL Conversion factors: 1 qt L 1 qt 1 L 1000 mL 1 L qt mL

Dimensional Analysis Ex. 1 Use these conversion factors to convert between units qt 1 L qt = 946 mL 1000 mL 1 L 

Dimensional Analysis Ex. 2 You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3. Starting unit: Ending unit: Equalities: 19.3 g=1 cm 3, 2.2 lbs=1 kg, 1000 g=1 kg Conversion factors: 19.3 g 1 cm g 2.2 lbs 1 kg 2.2 lbs 1000 g 1 kg 1000 g pounds cm 3

Dimensional Analysis Ex. 2 Use these conversion factors to convert between units. 1.5 lb 1 kg 2.2 lb = 35 cm g 1 kg 1 cm g

Dimensional Analysis Ex. 3 You try! Temple football needs 550 cm for a 1st down. How many yards is this? Given: 1 in=2.54 cm 550 cm 1 in 2.54 cm = 6.0 yd 1 ft 12 in 1 yd 3 ft

Dimensional Analysis Ex. 4 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 1 piece 1.5 cm

Using Scientific Measurements

Accuracy and Precision Accuracy- measurement is close to the “right” or accepted value Precision-a set of measurements are close to each other

Percent Error Represents the accuracy of a measurement. Can be positive if your value is below the accepted value or negative if your value is high. (only positive for this class. See note) NOTE: Please perform percent error calculations with absolute value. You should NOT have a negative number. accepted value your value

Percent Error Example 1 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 %

Percent Error Example 2 The actual density of a certain material is 7.44 g/cm 3. A student measures the density of the same material as 7.30 g/cm 3. What is the percent error of the measurement? % error = 1.9 %

What are 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

Counting Significant Figures RULES for Counting Sig Figs (Table 2-5, p.47) 1. All nonzero numbers are significant. ex has 4 sig figs 2. Leading zeros with a decimal point are NOT significant ex has 2 sig figs Trailing zeros WITH a decimal ARE significant ex has 4 sig figs 3. Trailing zeros WITHOUT a decimal ARE NOT significant ex. 2,500 has 2 sig figs

, Counting Significant Figures Example 4 sig figs 3 sig figs 2 sig figs

Math with Significant Figures Calculating with Sig Figs RULE #4: 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

Math with Significant Figures Calculating with Sig Figs (con’t) RULE #5: 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  350 g 3.75 mL mL 7.85 mL 224 g g 354 g

Math with 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 Practice (15.30 g) ÷ (6.4 mL) = g/mL  18.1 g 18.9g g g 4 SF2 SF  2.4 g/mL 2 SF

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

Scientific Notation Practice 2,400,000  g kg 7  km 6.2  10 4 mm 2.4  10 6  g 2.56  kg km 62,000 mm