measurement cartoon courtesy of lab-initio.com. 2 types of measurement qualitative-a non-numerical...
TRANSCRIPT
MEASUREMENT
Cartoon courtesy of Lab-initio.com
2 types of measurement
Qualitative-a non-numerical description of matter.(ex: red stone, heavy brick, hot steel)
Quantitative- a numerical measure. It must include a number, followed by a unit.
(ex: 2.14 grams, 49.6 ml, 0.2500 kg)
Uncertainty in Measurement
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
Why Is there Uncertainty? Measurements are performed with instruments
No instrument can read to an infinite number of decimal places
Which of these balances has the greatest uncertainty in measurement?
Taking Measurements
When taking measurements:Read to the smallest increment(mark) on the
instrumentEstimate one digit past the smallest
increment(mark)
Reading the Graduated Cylinder
Liquids in glass and some plastic containers curve at the edges
Changing the diameter of the cylinder will change the shape of the curve
This curve is called the MENISCUS
Your eye should be level with the top of the liquid
Reading the Graduated Cylinder
You should read to the bottom of the MENISCUS
Use the smallest increments to find all certain digits, then estimate 1 more digit.
There are two unlabeled graduations below the meniscus, and each graduation represents 1 mL, so the certain digits of the reading are…
mL.
Estimate the uncertain digit and take a reading
The meniscus is about eight tenths of the way to the next graduation, so the final digit in the reading is .
The volume in the graduated cylinder is
0.8 mL
mL.
10 mL Graduated CylinderWhat is the volume of liquid in the graduate?
___mL
25mL graduated cylinder What is the volume of liquid in the graduate?
___mL
100mL graduated cylinder What is the volume of liquid in the graduate?
____mL
What is this reading?
Practice Reading the Graduated Cylinder
___ ml
What is this reading?
Practice Reading the Graduated Cylinder
____ ml
Measuring Liquid Volume
Imag
es
create
d a
t htt
p:/
/ww
w.s
tand
ard
s.d
fes.
gov.
uk/p
rim
ary
fram
ew
ork
/dow
nlo
ad
s/S
WF/m
easu
ring
_cylin
der.sw
f
What is the volume of water in each cylinder?
Pay attention to the scales for each cylinder.
Reading a graduated cylinderAll of the equipment below measures volume in mL but the scales for each are different.
___mL ____mL ___mL
Reading a BuretOn the graduated cylinder, zero
was at the bottom of the scale, with values increasing going up the cylinder. However, a buret has zero at the top with values increasing going down the scale.
Determine the scale. Read at the bottom of the
meniscus with your eye level with the liquid.
____mL
What is the volume in the buret?
What is the volume in the buret?
Online Practice
Reading a graduated cylinder http://w1imr.cnm.edu/apps/chemlab/reading_a_meniscus.swf
Reading a buret http://w1imr.cnm.edu/apps/chemlab/burette.swf
Reading a ruler http://w1imr.cnm.edu/apps/chemlab/reading_a_ruler.swf
Lets play darts!
Precision and AccuracyAccuracy how close a result is to its true value.
Precision refers to the repeatability of results.
Neither accurate nor
precise
Precise but not accurate
Precise AND accurate
Types of Error
Error- the difference between a measurement and the accepted value.
Random Error - measurement has an equal probability of being high or low.
Systematic Error – a repeated error, often resulting from poor technique or incorrect calibration.
Scientific Notation
In science, we deal with some very LARGE numbers:
1 mole = 602000000000000000000000
In science, we deal with some very SMALL numbers:
Mass of an electron =0.000000000000000000000000000000091 kg
Scientific Notation
Imagine the difficulty of calculating the mass of 1 mole of electrons!
0.000000000000000000000000000000091 kg x 602000000000000000000000
???????????????????????????????????
Scientific Notation:A method of representing very large
or very small numbers in the form:
M x 10n
M is a number between 1 and 10
n is the exponent
2 500 000 000
Step #1: Insert an understood decimal point
.
Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal point
123456789
Step #4: Re-write in the form M x 10n
2.5 x 109
The exponent is the number of places we moved the decimal.
0.0000579
Step #2: Decide where the decimal must end up so that one number is to its leftStep #3: Count how many places you bounce the decimal pointStep #4: Re-write in the form M x 10n
1 2 3 4 5
5.79 x 10-5
The exponent is negative because the number we started with was less than 1.
Convert each standard number to scientific
notation:
2000 g 0.972 m
880000 m 6.55 s
0.00821 kg 71.9 ms
96.3 g 8999 cm
0.000965 m 450 g
Convert each to floating decimal form:
7.00 x 102 m 17 x 100 cm
2.22 x 10-4 cm 3.00 x 108 m/s
9.45 x 10-8 m 6.02 x 1023 atoms
4.00 x 103 g 8.75 x 10-1 m
5.99 x 10-5 kg 6.78 x 10-6 m
Significant Figures-all the digits that are known to be true.
Rules for Counting Significant Figures - DetailsNonzero Digits(1-9) always count as significant figures.
3456 has 4 significant figures
Rules for Counting Significant Figures - Details
Zeros- Leading zeros never count as
significant figures.
0.0486 has3 significant figures
Rules for Counting Significant Figures - Details
Zeros- Captive
zeros(sandwiched zeros) always count as significant figures.
16.07 has4 significant figures
Rules for Counting Significant Figures - Details
ZerosTrailing zeros are significant only if the number contains a decimal point.
9.300 has4 significant figures
Rules for Counting Significant Figures - DetailsExact numbers have an infinite number of significant figures. They tend to be numbers of indivisible objects.
7 computers
or
1 inch = 2.54 cm, exactly
Sig Fig Practice #1How many significant figures in each of the following & which is the estimated digit?
1.0070 m 5 sig figs(0)
17.10 kg 4 sig figs(0)
100,890 L 5 sig figs(9)
3.29 x 103 s 3 sig figs(9)
0.0054 cm 2 sig figs(4)
3,200,000 2 sig figs(2)
Rules for Significant Figures in Mathematical Operations
Multiplication and Division: # sig figs in the answer equals the least number of sig figs used in the calculation.
6.38 cm x 2.0 cm =12.76 13 cm2 (2 sig figs)
Sig Fig Practice #2
3.24 m x 7.0 m
Calculation Calculator says: Answer
22.68 m2 23 m2
100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3
0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2
710 m ÷ 3.0 s 236.6666667 m/s 240 m/s
1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft
1.030 g ÷ 2.87 mL 0.358885017 g/mL 0.359 g/mL
Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: The number of decimal places in the answer equals the number of decimal places in the least accurate measurement.
6.8 g + 11.934 g =18.734 18.7 g (3 sig figs)
Sig Fig Practice #3
3.24 m + 7.0 m
Calculation Calculator says: Answer
10.24 m 10.2 m
100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm
713.1 L - 3.872 L 709.228 L 709.2 L
1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb
2.030 mL - 1.870 mL 0.16 mL 0.160 mL