Presentation on theme: "Chapter 3 Scientific Measurement"— Presentation transcript:
1 Chapter 3 Scientific Measurement Understand scientific notationState the results of calculations to the appropriate number of significant figuresConvert between metric unitsMatch units or instruments with the proper measurement
2 Understand scientific notation To convert a number into scientific notation;move the decimal point so only 1 non-zero digit is to the left of the decimal point.if you move the decimal point to the left, the power of 10 will be positive.if you move the decimal point to the right, the power of 10 will be negative.3,600 = 3.6 x 103= 7.52 x 10-55,732, = ?= ?
3 Understand scientific notation To convert a number out of scientific notation;if the power of 10 is positive move the decimal point to the right the power number of placesif the power of 10 is negative move the decimal point to the left the power number of places.8.1 x 10-5 =1.2 x 108 =x 104 = ?3.704 x 10-6 = ?Practice Problems Handout
4 State the results of calculations to the appropriate number of significant figures Accuracy: Measure of how close a measurement comes to the actual or true valuePrecision: Measure of how close a series of measurements are to one anotherError:Experimental value – accepted valuePercent errorerror x 100%accepted value
5 State the results of calculations to the appropriate number of significant figures (Stop: scientific notation and % error problems)A student measures the temperatureof boiling water. The thermometerreads 99.1 oC.What is the error?Accepted value of boiling point of water is oC99.1 oC oC = -0.9 oCWhat is the percent error?-0.9 oC x 100% = 0.9%100.0 oC
6 State the results of calculations to the appropriate number of significant figures Measured quantities in science have a degree of uncertainty due to theinstrument being used. The measured number has to reflect thatuncertainty. That is accomplished by using:Significant Figures (Sig Figs)In science, a measured quantity has two meanings:The numerical value (with the proper units)The sensitivity (uncertainty) of the measuring instrument: precisionThe number of sig figs is important in calculationsPg. 56: Figure 3.6
7 Rules for Counting Sig Figs State the results of calculations to the appropriate number of significant figuresRules for Counting Sig FigsEvery nonzero digit represented in a measurement is significant.24.7 m has 3 sig figshas 4 sig figshas ? sig figshas ? sig figsZeros appearing between non zero digits are significant.7003 has 4 sig figshas 5 sig figshas ? sig figshas ? sig figs
8 Rules for Counting Sig Figs State the results of calculations to the appropriate number of significant figuresRules for Counting Sig FigsZeros ending a number to the right of the decimal point are significant23.80 has 4 sig figshas 6 sig figs1, has ? sig figshas ? sig figsZeros starting a number or ending the number to the left of the decimal point are not counted as significant16000 has 2 sig figshas 4 sig figs870,600 has ? sig figshas ? sig figs
9 Unlimited number of Sig Figs State the results of calculations to the appropriate number of significant figuresUnlimited number of Sig FigsSpecific whole numbers that are counted (vs measured) have unlimited numbers of significant figures.23 people4 fume hoodsExactly defined quantities have unlimited numbers of significant figures.1 minute = 60 seconds10 mm = 1 cm
10 General Rule for Counting Sig Figs State the results of calculations to the appropriate number of significant figuresGeneral Rule for Counting Sig Figs1. Start on the left with the first nonzero digit.2. End with the last nonzero digit OR with the last zero that ends the number to the right of the decimal point
11 Sig Figs in Calculations State the results of calculations to the appropriate number of significant figuresSig Figs in CalculationsAn answer cannot be more precise than the least precise measurementfrom which it was calculated!thereforeAny mathematical calculation involving measured quantities must berounded off to reflect the precision of the measurement!
12 Sig Fig Practice Problems How many sig figs in each measurement?meters metersmeters meter sticks3. 40,506 meters metersx 104 metersunlimited
13 Sig Fig Practice Problems How many sig figs:meters metersmeters metersRound each number to the number of sig figs shown:meters (4) meters (2)
14 Practice ProblemsRound each to 2 sig figs and write in scientific notation.meters x 108 metersmeters meters8.71 x x 108 m1.55 x 10-2 m x 103 mGo to Sig fig HO
15 State the results of calculations to the appropriate number of significant figures Sig Figs in Calculations: Addition & SubtractionThe answer to an addition or subtraction calculation must be rounded to the same number of decimal places as the measurement with the least number of decimal places.12.52 m m m = m12.52 has 2 decimal places; has 1 decimal place; 8.24 has 2 decimal placesThe answer is rounded off to 1 decimal place = mPractice problems Pg. 60: 9,10 on over head
16 State the results of calculations to the appropriate number of significant figures Sig Figs in Calculations: Multiplication & DivisionThe answer to a multiplication or division calculation must be rounded to the same number of significant figures as the measurement with the least number of significant figures.7.55 m x 0.34 m = m27.55 has 3 sig figs; 0.34 has 2 sig figsThe answer must be rounded to 2 sig figs = 2.6 m2Practice: Pg. 61: Sample Problem 3-4, 11,12
17 Density Density is the ratio of an object’s mass to its volume. Density= Mass/VolumeD = m/Vunits = g/cm3 (solid & liquid) or g/L (gases)Ex: a piece of lead has a volume of 10.0 cm3 and a mass of 114 g, what is it’s density?114g/ 10.0cm3 = 11.4 g/cm3
18 Density Solving for other variables: V = m/D What is the volume of a 68g bar of silver with a density of 10.5 g/cm3?M= D x VThere are two balloons, 10.0 L each, one contains helium (D=0.179 g/L), the other contains air (D=1.29g/L). How much less does the helium balloon weigh?GO TO DENSITY PRACTICE PROBLEM HO
20 Convert between metric units Quantity SI Unit Non-SI Unit InstrumentLength meter (m) RulerMass gram (g) BalanceTemperature Kelvin (K) oCelsius ThermometerVolume cubic meter liter Graduated CylinderBuretEnergy joule calorie CalorimeterAmount of molesubstance
21 Convert between metric units Metric Prefixeskilo hecto deka one deci centi milli1,(m,g,L)Mega Micro1,000, ,000,1Kids have dropped over dead converting metrics
22 Convert between metric units Metric ConversionsMoving the decimal pointIf the unit is the same, use the saying to move the decimal (KHDODCM)Convert 4.15 kg to cg:Start at K and move to c. The decimal will be moved 5 places to the right to give 415,000 cgConvert 3,470 mL to L:Start at m and move to o. The decimal will be moved 3 places to the left to give 3.47 LConvert 3.00 cm to mm:Start at c and move to m. The decimal will be moved 1 place to the right to give 30.0 mm (include all sig figs!)Convert 756 g to mL:Can’t be done due to different units!
23 Metric Practice Problems Convert the following on your own paper:1) grams to milligrams2) kilometers to meters3) 6089 milliliters to kiloliters4) convert 12.5 cm3 (centimeter cubed) to ml (milliliter)Answers: 1) mg 2) 4.56 m 3) kl4) 12.5 ml = 12.5 cm3 because 1ml = 1cm3
24 Convert between metric units Volume Measurements & ConversionsMetric volumes come in two forms: Liters or cubic metersConversion between forms: 1 L = 1 dm3 and 1 mL = 1 cm3Convert 3.45 L to cm3:3.45 L = 3,450 mL = 3,450 cm3Convert dm3 to mL:0.784 dm3 = L = 784 mLConversion within cubic form: 1 dm3 = 1,000 cm3When converting within cubic volumes, multiply the number of places the decimal is moved by 3Convert 2.56 m3 to cm3:Move the decimal two places to the right x 3 so a total of 6 places so 2,560,000 cm3GO to Metric HO
25 TemperatureTemperature is the measure of kinetic energy of particles in matter.Temperature determines the direction of heat transfer.Almost all substances expand with increasing temperature.
26 TemperatureThe Celsius scale sets the freezing point of water at 0°C and the boiling point at 100°C.The Kelvin scale sets 0 K at absolute zero (the ° symbol is not used).One degree on the Kelvin scale is equal to one degree on the Celsius scale.0 K = -273°C 0°C = 273 K K = °C + 273
27 Temperature Examples: Liquid nitrogen boils at 77.2 K. What is this temperature in °C?Silver melts at 960.8°C and boils at 2212°C. What is this temperature in degrees Kelvin?
28 Temperature Examples: Liquid nitrogen boils at 77.2 K. What is this temperature in °C? – 273 = -196Silver melts at 960.8°C and boils at 2212°C. What is this temperature in degrees Kelvin? Melting point: = 1234 K, boiling point: = 2485 K