Ch. 3, Scientific Measurement

Measurement Measurement: A quantity that has a number and a unit. Like 52 meters.

D. Scientific Notation Converting into Sci. Notation: –Move decimal until there’s 1 digit to its left. –Any number other than 0. –Places moved = exponent. –Large # (>1)  positive exponent Small # (<1)  negative exponent –Only include sig figs. 65,000 kg  6.5 × 10 4 kg

D. 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

D. Scientific Notation Calculating with Sci. Notation (5.44 x 10 7 g) / (8.1 x 10 4 mol) = Type of your calculator: 5.44 EE 7 / 8.1 EE 4 = = 670 g/mol = 6.7 x 10 2 g/mol

A. 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

Accuracy vs. Precision *Accuracy: How close a measurement comes to the correct value. *Precision: How close a series of measurements are to one another. – Consistency

Determining Error of a measurement Error = Experimental Value - Accepted Value – Can be positive or negative Percent Error = error / accepted value * 100% – or – Always positive Example, you measured 99 cm, but it is 100 cm. 99 cm – 100 cm 100 cm x 100 x 100 = 1% error

C. Significant Figures Indicate precision of a measurement. Recording Sig Figs –Sig figs in a measurement include the known digits plus a final estimated digit –(See page 24) 2.32 cm

1) How many sig figs after we estimate? –3.2 2) Now how many? –3.13

Rules for Sig Figs Non-Zero Numbers are always significant – Ex).236 m has 3 sig figs. Zeros between non-zero numbers are significant. – Ex) 7003 m and m each have 4 sig figs. Leftmost zeros are not significant – Ex) m, 0.42 m, and.073 m each have 2 sig figs. Rightmost zeros are significant IF they come before or after a decimal. – Ex) m, m, and m each have 4 sig figs. Rightmost zeros with no decimal points are not significant. Ex) 300 m has 1 sig fig. **The number of left handed people in the class is insignificant compared to the number of right handed people

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

Is a Zero a Significant Number or Not? 504 L.06 mL 50.0 m 7,000 km YES – 3 sig figs NO – 1 sig figs YES – 3 sig figs NO – 1 sig fig

C. 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

C. 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  7.9 mL 3.75 mL mL 7.85 mL

C. 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

In this class, delay rounding until the very end. 1.8 × 2.10 × Rounding: 1.8 x 2.10 = 3.8 x = 5.9 Round at end: 1.8 x 2.10 x = = 5.8

C. 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

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

Temperature: Celsius and Kelvin are units of temperature that are the same, just shifted. K = C Water freezes at 0 C and at 273 K. Absolute Zero = 0 K; K will never be negative. Convert 15 C to K = Convert 321 K to C = 288 K 48 C

E. SI Units mega-M10 6 deci-d10 -1 centi-c10 -2 milli-m10 -3 PrefixSymbolFactor micro-  nano-n10 -9 pico-p kilo-k10 3 BASE UNIT

Different way of looking at it… 1 km = 1000 m 1 m = 10 dm 1 m = 100 cm 1 m = 1000 mm 1 mm = 1000 um

F. 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

Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

Basic Algebra Review Whatever you do to one side, you do to the other =

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 = 11,220g  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

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 NUMBER UNIT NUMBER UNIT 532 m = _______ km 0.532

SI Unit Conversions King __doofus can milk many newts. k__ d c m m n kilo, deci, centi, milli, micro, nano What’s yours?

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 Lining up conversion factors: 1 in = 2.54 cm 2.54 cm 1 in = 2.54 cm 1 in 1 in = 1 1 =

Dimensional Analysis 5)Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? (1 in=2.54cm) 8.0 cm1 in 2.54 cm = 3.2 in cmin

Dimensional Analysis How many milliliters are in 1.00 quart of milk? (1L = qt) 1.00 qt 1 L qt = 946 mL qtmL 1000 mL 1 L 

Dimensional Analysis You have 1.5 pounds of gold. Find its volume in cm 3 if the density of gold is 19.3 g/cm 3. (1 kg = 2.2 lbs) lbcm lb 1 kg 2.2 lb = 35 cm g 1 kg 1 cm g

Dimensional Analysis Convert 60.0 km/hr into m/sec 60.0 km 1000 m 1 km = 16.7 m/sec 1 hr 60 min 1 min 60 sec 1 hr

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

Example Problems!!!

1. How many sig figs in: 1.480* E3 2. Perform these calculations and come up with answers that have the correct number of sig figs: E3 / E3 * 3 3. Convert 3.4 ug into kg. 4. Convert 7E3 cm into Mm. 5. What is the mass if a substance with a density of 4.5 g/L has a volume of 3 L?

6. How many sig figs in: Convert 3 kg into g. Convert 34 cm into m. Convert 4 m into cm. 8. You have a 4 kg box. You measure it to be 5.8 kg. What is the error? The % error? 9. What is the difference between accuracy and precision?

11. Put 5,009,000,000 into Scientific Notation 12. Put into Scientific Notation. 13. Put 8.7 * into a regular number.

14. Which is the largest amount? A. 2*10 2 g B. 30 kg C. 45 mg D. 190 g 15. Convert 40 Kelvin into Celsius 16. Convert 99 Celsius into Kelvin.