m easures : s ignificant figures, precision and accuracy dr. chin chu chemistry river dell high...
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MEASURES:SIGNIFICANT FIGURES, PRECISION AND ACCURACY
Dr. Chin Chu
Chemistry
River Dell High School
MEASUREMENTS
Temperature demonstration
What have been learned here? Human senses are not reliable indicator of
physical properties. We need instruments to give us unbiased
determination of physical properties. A system must be established to properly
quantify the measurements. Scales and units.
MEASUREMENTS
Definition – comparison between measured quantity and accepted, defined standards (SI).
Quantity: Property that can be measured and described by
a pure number and a unit that refers to the standard.
MEASUREMENT REQUIREMENTS
Know what to measure.
Have a definite agreed upon standard.
Know how to compare the standard to the measured quantity. Tools such as ruler, graduated cylinder, thermometer, balances and etc…
MEASUREMENTS – UNITS SI Units – (the metric system)
Universally accepted Scaling with 10
Base Units: Time (second, s) Length (meter, m) Mass (kilogram, kg) Temperature (Kelvin, K) Amount of a substance (mole, mol) Electric current (ampere, A) Luminous intensity (candela, cd)
MEASUREMENTS - TEMPERATURE Temperature Scales:
Celsius (°C, centigrade) Water freezing: 0 °C Water boiling: 100 °C
Kelvin (K, SI base unit of temperature) Same spacing as in Celsius scale. Conversion: Celsius + 273 = Kelvin
Fahrenheit (°F) Not the same spacing as the other two. Conversion: Fahrenheit = (5/9)(Celsius -32)
MEASUREMENTS – UNITS
Derived Units: Volume
Units: (length)3, such as cm3,m3, dm3 (liter)
Density Defined as mass per unit volume the substance occupies.
volume
massdensity
depthheightlengthvolume
HOW RELIABLE ARE MEASUREMENTS?
Let’s use a golf anaolgy
Accurate? No
Precise? Yes
Accurate? Yes
Precise? Yes
Precise? No
Accurate?Maybe?
Accurate? Yes
Precise? We cant say!
IN TERMS OF MEASUREMENT
Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across.
Were they precise? Were they accurate?
ASSESSING UNCERTAINTY
The person doing the measuring should asses the limits of the possible error in measurement
SIGNIFICANT FIGURES (SIG FIGS)
How many numbers mean anything When we measure something, we can (and do)
always estimate between the smallest marks.
21 3 4 5
SIGNIFICANT FIGURES (SIG FIGS)
The better marks the better we can estimate. Scientist always understand that the last number
measured is actually an estimate
21 3 4 5
object
mm
SIGNIFICANT DIGITS AND MEASUREMENT
Measurement Done with tools The value depends on the smallest subdivision
on the measuring tool
Significant Digits (Figures): consist of all the definitely known digits plus one
final digit that is estimated in between the divisions.
SIGNIFICANT FIGURES
Only measurements have significant figures. Counted numbers and defined constants are exact
and have infinite number of significant figures. A dozen is exactly 12 1000 mL = 1 L
Being able to locate, and count significant figures is an important skill.
Measured Value
Uncer- tainty
Ruler Division
Known digits
Estimated digit
1.07 cm +/-0.01 cm
0.1 cm 1, 0 7
3.576 cm +/-0.001 cm
0.01 cm 3,5,7 6
22.7 cm +/- 0.1 cm 1 cm 2, 2 7
Significant Figures: Examples
SIGNIFICANT FIGURES: EXAMPLES
What is the smallest mark on the ruler that measures 142.15 cm? ____________________
142 cm? ____________________
140 cm? ____________________
Does the zero count? We need rules!!!
RULES OF SIGNIFICANT FIGURES
Pacific:
If there is a decimal point present start counting from the left to right until encountering the first nonzero digit. All digits thereafter are significant.
Atlantic:
If the decimal point is absent start counting from the right to left until encountering the first nonzero digit. All digits are significant.
RULES OF SIGNIFICANT FIGURES - EXAMPLES
Pacific Ocean Atlantic OceanExample 1
Example 2
0.00078638
decimal point
7863800078638
No decimal point
78638
ROUNDING RULES
Rounding is always from right to left. Look at the number next to the one you’re
rounding. 0 - 4 : leave it
5 - 9 : round up
With one exception: when the number next to the one you’re rounding is 5 and not followed by nonzero digits (a.k.a. followed by all zeros) – round up if the number (rounding to) is odd; don’t do anything if it is even.
2.536
ROUNDING RULES - EXAMPLES
Example 1 2.532
Last significant digit
< 5 2.532.532leave it
Example 2 2.536
Last significant digit
> 5round up
2.54
2.5351Example 3 2.5351
Last significant digit
> 5round up
2.54
2.5350Example 4 2.5350
Last significant digit
the exception round up
2.54odd
MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES
Addition and Subtraction
The answer must have the same number of digits to the right of the decimal point as the
value with the fewest digits to the right of the decimal point.
Why?
The result from the addition or subtraction would have the same precision as the least
precise measurement.
MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES
Addition and Subtraction
Example:
28.0 cm23.538 cm25.68 cm77.218 cm
28.0 cm 23.538 cm 25.68 cm
1. Arrange the values so that decimal points line up.
4. Round the answer to the same number of places.
2. Do the sum or subtraction.
3. Identify the value with fewest places after decimal point.
77.2 cm
MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES
Multiplication and Division
The answer must have the same number of significant figures as the measurement with
the fewest significant figures.
MATHEMATICAL OPERATIONS INVOLVING SIGNIFICANT FIGURES
Multiplication and Division
Example:
16924.76352 cm3
1. Carry out the operation.
2. Identify the value with fewest significant figures.
3. Round the answer to the same significant figures.
28.0 cm 23.538 cm 25.68 cm
28.0 cm23.538 cm25.68 cm
16900 cm3
3