K (what do you know
About Measurement)
W (what do
L (what
you want to have you
know
learned)
about
Measurement
In the context of the scientific method, precision and
accuracy have two distinctly different meanings.
The accuracy of a measurement system is the degree
of closeness of measurements of a quantity to its
actual (true)value.
 The precision of a measurement system is the degree
to which repeated measurements under unchanged
conditions show the same results.
See dartboard (p. 44)
 A measurement system can be accurate but not
precise, precise but not accurate, neither, or both.

www.yorku.ca/psycho/en/pics_en/postscript_f1.gif
% error = measured – accepted
accepted
X 100
p. 45 #1 practice problem
Find the % error if a mass measurement is 17.7
grams when the correct mass is 21.2 grams.
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A liquid’s volume is measured in a beaker as
40 mL. It is then measured in a graduated
cylinder as 45.5 mL. Find the % error.
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P. 45 # 1—2
p. 60 #35—37
1.
2.
3.
4.
5.
6.
7.
8.
0.9%
0.4%
3.5%
9.3%
1.7%
3.7%
0.3%
10.4%
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MEASUREMENT WARM UP
1. Based on the following data collected,
comment on this person’s accuracy &
precision:
***Volume in beaker
trial 1= 30.0 mL
Trial 2 = 31.0
Trial 3= 31. 5
***Volume in cylinder =
45.5 mL
2. Calculate % error:
A student measures mass as 50.9 grams.
The instructor measures 55.9 grams.
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1. high precision; low accuracy
2. 8.9%
Write a paragraph to your friend explaining to
him or her the difference between accuracy
vs. precision. Include an example using the
dartboard analogy. (refer to p. 44 if needed)
CALCULATE % ERROR FOR THE FOLLOWING:
1. A student measures the volume of a cube to be 20.5 cubic
centimeters. He checks this against the correct volume
which is 25 cubic centimeters.
2. A liquid’s volume is 35 mL in a graduated cylinder, while in
a beaker the volume is 25 mL.
3.
Comment
On precision
And accuracy
For picture D.
http://www.brookscole.com/math_d/sp
ecial_features/ext/internet_activities/
matovina/metric
ONLY COMPLETE 1—6 and #8 TODAY
USE YOUR OWN NOTEBOOK PAPER
Why is the metric system of measurement
(which uses meters, liters, grams, etc.)
preferred AND easier to use rather than the
English system of measurement (which uses
pounds, feet, etc.)?
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1
1
1
1
1
foot. = 12 inches
pound = 16 ounces
cup = 8 ounces
yard = 3 feet
mile = 5280 feet
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Also known as the SI based system
(International System of Measurements)
It is more preferred rather than the English
system of measurements because it is based
on units of 10.
Measurement systems are all based on
“standards” which are physical
representations for each measurement unit.
We will learn about the prefixes “Tera”
through “pico”. (see chart)
Mass = gram
Distance = meter
Volume = liters or cubic meter
Time = seconds
Temperature = Kelvin
Amount of a substance = mole
Electric current = ampere
Light intensity = candela
Area = square meter
Energy = joule
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1 KILOmeter = ________________meters
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1 CENTIgram = ______________________grams
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1 millisecond = __________________seconds
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THE
GREAT
MIGHTY
king
henry
died
by
drinking
chocolate
milk
maybe
not
pasteurized
mg
kL
Mm
mm
um
m
Name 3 basic metric units.
Name 2 prefixes AND give their symbol.
Name 1 thing you know about a “standard” of
measurement.
1. liquids—graduated cylinder (measures in
mL)
2. rectangular shaped solids- use a ruler for
length x width x height (measured in cubic
cm or cm3 or cc)
3. Irregular shaped solids—water displacement
***VOLUME—the amount of space something
takes up
25 mL = ___________________cc (cm3)
25 cc = ________________________L
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1—12, 15, 16
Describe how you would take the volume of a
glass of water, a rectangular block, and a
marble. Also, tell what units that you would
use to measure each.
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WRITING ASSIGNMENT:
(1-2 paragraphs)
Discuss the differences between area &
volume. Include in your discussion: ways
they are measured, units which they are
measured in, and tools used to measure
them. Also, remember the different methods
for measuring volume.
% ERROR/METRICS
 1. A lab tech measures the boiling point of
water to be 99.5 C. The true boiling pt of
water is 100.0 C. Calculate the % error.
(SHOW WORK!!)
 2.
0.0075 g = ______________________ng
 3.
3400 kg = ____________________Mg
 4.
258 daL = _______________________mL
 5.
534 L = __________________cm3
1.
2.
3.
4.
5.
99.5 – 100.0
x 100 = 0.5%
100.0
7 500 000 ng
3.4 Mg
2 580 000 mL
534 000 cc (mL)
In a paragraph, describe how mass, volume,
length, and temperature are measured.
PART III #8 SHOW WORK FOR % ERROR
Accepted values:
Bottle = 7.095 grams
Clamp = 75.069 grams
Domino = 5.371 grams
Stopper = 7.090 grams
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METRIC WARMUP
GIVE THE SYMBOL FOR EACH UNIT:
1. Micrometer
2. Meter
3. Kiloliter
4. Megameter
5. millimeter
WHAT QUANTITY DO THESE UNITS MEASURE?
7. meter
8. cc
9. liter
10. gram
11. Cm3
12. Square meter
PERFORM THESE METRIC CONVERSIONS:
13.
14.
15.
16.
2.67 ng = _______________pg
34000 m = ______________Mm
50 cc =_______________mL
3 L = __________________cm3
This is done when BOTH units have the SAME
exponent (squared to squared or cubed to
cubed)
 Ex: 100 cm2 = _______________m2
cm to m is normally 2 spaces left, so multiply
this 2 spaces x the exponent of 2 = total of 4
spaces left
Ex: 0.0075 Mm3 = ________________km3
Mm to km is normally 3 spaces right, so
multiply by exponent of 3 = 9 spaces right
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1.
55 cc = ______L
2.
0.00035 Mm = _________m
3.
675 dL =____________kL
4. What do millimeters measure?
5. What do kilograms measure?
6. What do liters measure?
7. What do cubic millimeters measure?
8. What do square centimeters measure?
9. Which is larger: 250 cc or 0.5 L?
10. Find the area of a box measuring 5 cm by 8 cm.
11. Does milli make the base unit larger or smaller?
12. Find the volume of a rock that’s dropped in 25
mL of water and the level then rises to 38 mL.
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1. 0.055 L
2. 350 m
3.
0.0675 kL
4. length
5. mass
6. volume
7. volume
8. area
9. 0.25 L or 0.5 L
10. 5 cm x 8 cm = 40 cm2
11. smaller
12. 38 – 25 = 13 mL
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BOOK PROBLEMS (% error, metrics,
accuracy/precision)
p. 59 #1, 4, 7, 8 ab, 9 ab, 16, 20, 21, 24, 25,
37
p. 63 #1, 3, 4, 6, 7, 8
Explain why error always exists in
measurement.
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Significant figures help scientists be able to
do the same thing when taking
measurements and doing calculations.
SEE P. 46
1.
2.
3.
4.
Digits from 1-9 are always significant.
Zeros between two other significant digits
are always significant
Final zeros to the right of the decimal place
are significant.
Zeros used solely for spacing the decimal
point (placeholders) are not significant
(Unless specifically measured and noted
with a line above the number).
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The letters "A" (decimal absent) and "P"
(decimal present) correspond to the "Atlantic"
and "Pacific" Oceans on a map.

Now, imagine an arrow being drawn from the
appropriate coast. Once the arrow hits a
NONZERO digit, this digit and all of the digits
after it are significant.
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Example 1. How many significant digits are
shown in the number 20 400 ? Well, there is
no decimal, so we think of "A" for
"Absent". This means that we imagine an
arrow coming in from the Atlantic ocean
20 400  this shows 3 significant numbers
as you do not count numbers until
you hit a significant digit
Modified from
http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm
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Example 2. How many significant digits are
shown in the number 0.090 ? Well, there is a
decimal, so we think of "P" for "Present". This
means that we imagine an arrow coming in
from the Pacific ocean.
0.090 This shows that the number has two
significant digits after the non zero
number is encountered
Modified from
http://www.fordhamprep.org/gcurran/sho/sho/lessons/lesson23.htm
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1.
2.
3.
4.
5.
6.
7.
8.
2300. m
2300 g
0.005 L
23.92 sec
40,060 kg
2005 moles
32.00 Kelvin
43.090 Mm
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1.
2.
3.
4.
5.
6.
7.
8.
P=4
A= 2
P=1
P=4
A=4
A=4
P=4
P=5
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TELL IF THE FOLLOWING ARE “ATLANTIC” OR
“PACIFIC” AND THEN TELL HOW MANY SIG
FIGS:
1. 0.0035 cm
7. 0.004 mg
2. 10.00 g
8. 549000 cm
3.
3400 m
9. 3000 g
4.
53.57 mm
10. 0.45670 nm
5.
40600 kg
11. 2734 km
6.
200.040 Mm
12. 5.070 sec
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TELL IF THE FOLLOWING ARE “ATLANTIC” OR “PACIFIC”
AND THEN TELL HOW MANY SIG FIGS:
1.
67. 930 g
2.
3.
4.
5.
6.
7.
8.
9.
10.
2600 m
0.0070 km
5030 cm
67.00 mm
3.69 sec
0.03 mm
1000 kg
1000. Mm
63.500 kg
You may ONLY do this to zeros in ATLANTIC
numbers
1. put a bar over the zero
2500—has 2 sig figs
How to make 3 sig figs??
How to make 4 sig figs??
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Put a decimal at the end (making it a pacific #)
2500
2500.
2.
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TELL HOW MANY SIG FIGS
(1ST DECIDE IF A or P)
1. 21.34 g
2. 52.340 g
3. 28,007 L
4. 80.00 m
5. 0.0025 g
6. 23,000 cm
7. 28, 875 mm
8. 505,100 g
9. 0.050 L
IN EACH:
10.
11.
12.
13.
14.
15.
16.
17.
18.
51.200 g
6050 m
2000 L
40.50 cm
0.192 m
3000. L
30 mm
30,650 Mm
0.00500 g
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1. 4
2. 5
3. 5
4. 4
5. 2
6. 5
7. 5
8. 5
9. 2
10. 5
11. 3
12.
When trying to do this, move through the
number from left to right.
Ex: Round to 1 sig fig:
2300
0.0897
5.9
Round to 2 sig figs:
2895
0.0956
Round to 3 sig figs:
2895
0.6
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TELL HOW MANY SIG FIGS ARE IN EACH--1st decide if
A or P:
1.
0.00306
5. 3000.
2.
0.003060
6. 43.06
3.
4300
7. 3.020
4.
4060
8. 5000
ROUND EACH TO 2 SIG FIGS:
1.
0.0357
4. 657
2.
2350
5. 0.0695
3.
90.34
6. 0.7
ROUND EACH TO 1 SIG FIG:
1.
369
3. 0.0078
2.
20.47
4. 379.5
9. 2.0
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1.
2.
3.
4.
3
4
2
4
1. 0.036
2. 2400
3. 90.
1.
2.
3.
4.
400
20
0.008
400
5.
6.
7.
8.
4
4
4
1
4. 660
5. 0.070
6. 0.70
9. 2
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Round answer to the FEWEST DECIMAL
PLACES that are in the problem
10.711 g
+3.23 g
4 mL
-3.4 mL
5.75 cm
+2.976 cm
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1.
2.
3.
13.941 = round to 2 dec. = 13.94 g
0.6 = round to 0 dec. = 1 mL
8.726 = round to 2 dec. = 8.73 cm
answer to the FEWEST SIG
FIGS that are in the problem
 Round
2.32 cm x 77.96 cm =
62.0 g / 2.000 mL =
1.805 m x 6.0 m =
 1.
 2.
 3.
180.8672=round to 3 sig
figs = 181 cm2
31=round to 3 sig figs =
31.0 g/mL
10.83= round to 2 sig figs
= 11m2
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Give any 3 measurements and tell how many
sig figs are in each.
Describe the 2 different ways to round
(add/subtract VS. Multiply/divide)
Name 1 way to make zeros significant when
they’re not to begin with.
 1—34
EVEN
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22. 30.647 = 30.6 grams
24. 9.2946 = 9.29 L
26. 29.56 = 30 sec
28.
1.967 = 2 g/mL
30. 0.022737 = 0.023 sq inches
32. 0.25 = 0. 250 kg/L
34. 0.012049 = 0.01205 Mm2
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 2.
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 5.
5.0 m X 457 m=
16.56 g + 13 g =
5.60 g / 22.4 L =
0.059 g / 0.03 L =
14.26 cm - 4.9654 cm =
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2285 = round to 2 sig figs = 2300 m2
29.56 = round to no decimal places = 30 g
0.25 = round to 3 sig figs = 0.250 g/L
1.966666 = round to 1 sig fig = 2 g/mL
9.2946 =round to 2decimal places = 9.29 cm
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P. 50 #1—3

P. 57 #3—4
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Why would someone want to put a
measurement into scientific notation?

Reduces the number of zeros in really big or
really small numbers
The number in front determines the number
of sig figs
 Starting out, the decimal MUST be written to
the right of the first nonzero number in order
to be in correct scientific form; then,
depending on the exponent, it can be moved
left or right to convert to a regular number.
5.64 x 104
(correct form with 3 sig figs)
0.0035 x 102 (incorrect form) Why??
340 x 103
(incorrect form) Why??
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6.023 x 1023  4 sig figs
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6.67 x 10-11  3 sig figs

2.00 x 10-3  3 sig figs
 In
your calculator, 3.05 x
109 may appear:
3.05
3.05
3.05
E9
EE 9
9
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If the exponent is POSITIVE, move decimal
that many places to the RIGHT.
Ex: 3.450 x 103

***Remember to keep SIG FIGS the same!!
If the exponent is NEGATIVE, move decimal
that many places to the LEFT.
Ex: 6.090 x 10-3
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***Remember to keep SIG FIGS the same!!
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 1.
4.560 x 105 =
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 2.
3.9 x 10-3 =
 3.
5.0 x 100 =
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Remember that the decimal must be moved
to the right of the first nonzero digit. Also,
remember to keep SIG FIGS the same.
If the number is greater than 1 to start with,
use a positive exponent.
Ex: 305,000
If the number is less than 1 to start with, use
a negative exponent.
Ex:0.004060
 1.
456,000. =
 2.
0.003400 =
 3.
67000 =
 SIG
FIGS---EVEN (OPTIONAL)
 SCIENTIFIC
NOTATION--EVEN
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WARM UP
PUT INTO SCIENTIFIC NOTATION:
1.
0.0060
2.
23500
PUT INTO STANDARD FORM (REGULAR
NUMBER)
3.
3.50 X 102
4.
6.788 X 10-3
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P. 57 #6
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P. 60 #43—45
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p.
p.
p.
p.
p.
p.
48
57
60
31
42
59
#1-2
#1-3
#29, 38
#2
#1-3
#6-9, 16, 20, 21, 23, 25a, 38, 50, 51
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WHAT TO STUDY FOR MEASUREMENT TEST
1. Qualitative vs. quantitative measurement
2. What’s the purpose of a standard in measurement
3. Basic units for length, time, volume, mass, and temp.
4. Metric prefix symbols, numerical meanings, and
exponent meanings
5. Metric conversions (normal, cc = mL, and exponent
ones)
6. Units for area and volume
7. 3 ways to measure volume
8. % error
9. Accuracy vs. precision
10. Mass vs. weight
11. Counting # of sig figs AND calculation rules for sig
figs
12. Scientific notation into standard form (and vice-versa)
13. Vocabulary sheet
14. Reading metric tools
15. Measurement video ?s