measurement
DESCRIPTION
Measurement. Quantitative Observation Comparison Based on an Accepted Scale e.g. Meter Stick Has 2 Parts – the Number and the Unit Number Tells Comparison Unit Tells Scale. Scientific Notation. Technique Used to Express Very Large or Very Small Numbers Based on Powers of 10 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/1.jpg)
1
Measurement
• Quantitative Observation
• Comparison Based on an Accepted Scale– e.g. Meter Stick
• Has 2 Parts – the Number and the Unit– Number Tells Comparison– Unit Tells Scale
![Page 2: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/2.jpg)
2
Scientific Notation
• Technique Used to Express Very Large or Very Small Numbers
• Based on Powers of 10
• To Compare Numbers Written in Scientific Notation– First Compare Exponents of 10– Then Compare Numbers
![Page 3: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/3.jpg)
3
Writing Numbers in Scientific Notation1 Locate the Decimal Point2 Move the decimal point to the right of the non-
zero digit in the largest place– The new number is now between 1 and 10
3 Multiply the new number by 10n
– where n is the number of places you moved the decimal point
4 Determine the sign on the exponent n– If the decimal point was moved left, n is +
– If the decimal point was moved right, n is –
– If the decimal point was not moved, n is 0
![Page 4: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/4.jpg)
4
Writing Numbers in Standard Form
1 Determine the sign of n of 10n
– If n is + the decimal point will move to the right– If n is – the decimal point will move to the left
2 Determine the value of the exponent of 10– Tells the number of places to move the decimal
point
3 Move the decimal point and rewrite the number
![Page 5: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/5.jpg)
5
Related Units in the Metric System
• All units in the metric system are related to the fundamental unit by a power of 10
• The power of 10 is indicated by a prefix
• The prefixes are always the same, regardless of the fundamental unit
![Page 6: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/6.jpg)
6
Table 2.2: The Commonly used Prefixes in the Metric System
![Page 7: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/7.jpg)
7
Length• SI unit = meter (m)
– About 3½ inches longer than a yard• 1 meter = one ten-millionth the distance from the North Pole to the
Equator = distance between marks on standard metal rod in a Paris vault = distance covered by a certain number of wavelengths of a special color of light
• Commonly use centimeters (cm)
– 1 m = 100 cm
– 1 cm = 0.01 m = 10 mm
– 1 inch = 2.54 cm (exactly)
![Page 8: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/8.jpg)
8
Table 2.3: The Metric System for Measuring Length
![Page 9: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/9.jpg)
9
Figure 2.1: Comparison of English and metric units for length on a ruler
![Page 10: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/10.jpg)
10
Volume• Measure of the amount of three-dimensional space occupied by a
substance• SI unit = cubic meter (m3)• Commonly measure solid volume in cubic centimeters (cm3)
– 1 m3 = 106 cm3 – 1 cm3 = 10-6 m3 = 0.000001 m3
• Commonly measure liquid or gas volume in milliliters (mL)– 1 L is slightly larger than 1 quart– 1 L = 1 dm3 = 1000 mL = 103 mL – 1 mL = 0.001 L = 10-3 L– 1 mL = 1 cm3
![Page 11: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/11.jpg)
11
Figure 2.2: Cubes
![Page 12: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/12.jpg)
12
Figure 2.3: A 100-ml Graduated Cylinder
![Page 13: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/13.jpg)
13
Mass
• Measure of the amount of matter present in an object
• SI unit = kilogram (kg)• Commonly measure mass in grams (g) or
milligrams (mg)– 1 kg = 2.2046 pounds, 1 lbs.. = 453.59 g– 1 kg = 1000 g = 103 g, 1 g = 1000 mg = 103 mg– 1 g = 0.001 kg = 10-3 kg, 1 mg = 0.001 g = 10-3 g
![Page 14: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/14.jpg)
14
Figure 2.4: An electronic analytical
balance used in chemistry labs
![Page 15: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/15.jpg)
15
Uncertainty in Measured Numbers
• A measurement always has some amount of uncertainty
• Uncertainty comes from limitations of the techniques used for comparison
• To understand how reliable a measurement is, we need to understand the limitations of the measurement
![Page 16: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/16.jpg)
16
Reporting Measurements
• To indicate the uncertainty of a single measurement scientists use a system called significant figures
• The last digit written in a measurement is the number that is considered to be uncertain
• Unless stated otherwise, the uncertainty in the last digit is ±1
![Page 17: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/17.jpg)
17
Figure 2.5: Measuring a Pin
![Page 18: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/18.jpg)
18
Rules for Counting Significant Figures
• Nonzero integers are always significant• Zeros
– Leading zeros never count as significant figures– Captive zeros are always significant– Trailing zeros are significant if the number has
a decimal point
• Exact numbers have an unlimited number of significant figures
![Page 19: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/19.jpg)
19
Exact Numbers• Exact Numbers are numbers known with certainty • Unlimited number of significant figures• They are either
– counting numbers• number of sides on a square
– or defined• 100 cm = 1 m, 12 in = 1 ft, 1 in = 2.54 cm
• 1 kg = 1000 g, 1 LB = 16 oz
• 1000 mL = 1 L; 1 gal = 4 qts.
• 1 minute = 60 seconds
![Page 20: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/20.jpg)
20
Calculations with Significant Figures
• Calculators/computers do not know about significant figures!!!
• Exact numbers do not affect the number of significant figures in an answer
• Answers to calculations must be rounded to the proper number of significant figures– round at the end of the calculation
![Page 21: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/21.jpg)
21
Rules for Rounding Off
• If the digit to be removed• is less than 5, the preceding digit stays the
same• is equal to or greater than 5, the preceding
digit is increased by 1
• In a series of calculations, carry the extra digits to the final result and then round off
• Don’t forget to add place-holding zeros if necessary to keep value the same!!
![Page 22: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/22.jpg)
22
Multiplication/Division with Significant Figures
• Result has the same number of significant figures as the measurement with the smallest number of significant figures
• Count the number of significant figures in each measurement
• Round the result so it has the same number of significant figures as the measurement with the smallest number of significant figures
4.5 cm x 0.200 cm = 0.90 cm2
2 sig figs 3 sig figs 2 sig figs
![Page 23: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/23.jpg)
23
Adding/Subtracting Numbers with Significant Figures
• Result is limited by the number with the smallest number of significant decimal places
• Find last significant figure in each measurement
• Find which one is “left-most”• Round answer to the same decimal place
450 mL + 27.5 mL = 480 mLprecise to 10’s place precise to 0.1’s place precise to 10’s place
![Page 24: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/24.jpg)
24
Problem Solving and Dimensional Analysis
• Many problems in chemistry involve using equivalence statements to convert one unit of measurement to another
• Conversion factors are relationships between two units– May be exact or measured– Both parts of the conversion factor should have the same
number of significant figures
• Conversion factors generated from equivalence statements– e.g. 1 inch = 2.54 cm can give or
in1cm54.2
cm54.2in1
![Page 25: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/25.jpg)
25
• Arrange conversion factors so starting unit cancels– Arrange conversion factor so starting unit is on
the bottom of the conversion factor
• May string conversion factors
Problem Solving and Dimensional Analysis
![Page 26: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/26.jpg)
26
Converting One Unit to Another
• Find the relationship(s) between the starting and goal units. Write an equivalence statement for each relationship.
• Write a conversion factor for each equivalence statement.
• Arrange the conversion factor(s) to cancel starting unit and result in goal unit.
![Page 27: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/27.jpg)
27
Converting One Unit to Another
• Check that the units cancel properly
• Multiply and Divide the numbers to give the answer with the proper unit.
• Check your significant figures
• Check that your answer makes sense!
![Page 28: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/28.jpg)
28
Temperature Scales• Fahrenheit Scale, °F
– Water’s freezing point = 32°F, boiling point = 212°F
• Celsius Scale, °C– Temperature unit larger than the Fahrenheit
– Water’s freezing point = 0°C, boiling point = 100°C
• Kelvin Scale, K– Temperature unit same size as Celsius
– Water’s freezing point = 273 K, boiling point = 373 K
![Page 29: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/29.jpg)
29
Figure 2.6: Thermometers based on the three temperature scales in (a) ice water and (b) boiling water
![Page 30: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/30.jpg)
30
Figure 2.7: The three major temperature scales
![Page 31: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/31.jpg)
31
Figure 2.8: Converting 70°C to units measured on the Kelvin scale
![Page 32: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/32.jpg)
32
Figure 2.9: Comparison of the Celsius and Fahrenheit scales
![Page 33: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/33.jpg)
33
Density• Density is a property of matter representing the mass per unit
volume
• For equal volumes, denser object has larger mass
• For equal masses, denser object has small volume
• Solids = g/cm3
– 1 cm3 = 1 mL
• Liquids = g/mL
• Gases = g/L
• Volume of a solid can be determined by water displacement
• Density : solids > liquids >>> gases
• In a heterogeneous mixture, denser object sinks
VolumeMass
Density
![Page 34: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/34.jpg)
34
Using Density in Calculations
VolumeMass
Density
DensityMass
Volume
Volume Density Mass
![Page 35: Measurement](https://reader036.vdocument.in/reader036/viewer/2022062801/56814413550346895db0b134/html5/thumbnails/35.jpg)
35
Figure 2.10: (a) Tank of water. (b) Person submerged in the tank, raising the level of the water.