Measuring
Measuring
Measuring
MKS system
MKS – Meter-Kilogram-Second
Historical Pt-Ir meter bars
U.S. National Kilogram (NIST)
Cesium Fountain Clock at NIST
Seven Fundamental units
Kilogram
Meter
Second
Candela
Ampere
Kelvin
Mole
Giga (G) = 109
Mega (M) = 106
kilo (k)
= 103
hecto (h) = 102
deka (da) = 101
deci (d) = 10-1
centi (c) = 10-2
milli (m) = 10-3
micro (m) = 10-6
nano (n) = 10-9
pico (p) = 10-12
The Metric System
Examples:
1 km = 1 X 103 m
1 nm = 1 X 10-9 m
1 Ms = 1 X 109 s
1 mL = 1 X 10-3 L
The Metric System
Examples:
600 nm
0.0055 Gs
5677 kg
=?m
=?s
=?g
The Metric System
Examples:
600 nm
0.0055 Gs
0.000567 kg
= 6 X 10-7 m
= 5.5 X 106 s
= 5.67 X 106 g
Metric Examples
a. How many meters is 55 cm?
b. How many milliters is 0.0250 liters?
c. How many kilograms is 13405 mg?
(0.013405 kg)
d. How many milliseconds is 0.0450
hectoseconds? (4500 ms)
Metric Practice Examples
4658 cm =
635 cm =
553 ms =
0.0023 kL =
0.468 cm =
7200 cs =
3498 s =
? km
? dam
? ds
? mL
? mm
? das
? hours
Metric Practice Examples
4658 cm =
635 cm =
553 ms =
0.0023 kL =
0.468 cm =
7200 cs =
3498 s =
0.04658 km
0.635 dam
5.53 ds
2300 mL
4.68 mm
7.2 das
0.9717 hours
Metric Example 5
How many square meters is 685 cm2?
685 cm2 1 X 10-2 m
1 cm
685 cm2 1 X 10-2 m 1 X 10-2 m
1 cm
1 cm
685 cm2 1 X 10-2 m 1 X 10-2 m = 0.0685 m2
1 cm
1 cm
Metric Example 6
How many square decimeters is 0.250 m2?
0.250 m2 1 dm
1X10-1 m
0.250 m2
1 dm
1 dm
1X10-1 m 1X10-1 m
0.250 m2
1 dm
1 dm = 25.0 dm2
1X10-1 m 1X10-1 m
Metric Example 7
How many cubic centimeters (cm3) is
0.00453 m3?
(Ans: 4520 cm3)
Challenge
Problem
The tallest building in
the world is the
Burj Kalifa, Dubai.
It is 828 meters
tall. How many
feet is that?
(1 inch = 2.54 cm)
Metric Example 9
Convert 22 miles/hour to m/s.
22 miles
1 hr
1.61 km 1X103m 1 hr 1 min = 9.8 m/s
1.00 mile
1 km 60 min 60 s
Metric Example 10
Convert 200 cm/s to miles/hour.
200 cm
1s
1X10-2 m 1 km 1.00 mile 60 s
1 cm
1X103 m 1.61 km 1 min
60 min
1 hr
= 4.47 miles/hr
Metric Practice Examples
55 mi/hr
55 mi/hr
65 miles/hr
400 cm/s
 km/hr
 meters/min
 meters/s
 miles/hr
Metric Practice Examples
55 mi/hr
55 mi/hr
65 miles/hr
400 cm/s
 89 km/hr
 1476 meters/min
 29.1 meters/s
 8.94 miles/hr
Accuracy and Precision
Accuracy
– how close the average of a set of measurements
is to the true value
– Measured using Percent Error
% Error = Experimental – Accepted X 100
Accepted
Precision
– How close a set of measured values are to one
another
– Measured using Range
– Highest - lowest
Accuracy and Precision
Students did trials to measure the density of a
metal. The accepted density is 7.2 g/cm3.
Were they accurate or precise?
Set 1
Set 2
Set 3
7.21 7.25 7.18
6.40 7.90 7.30
6.45 6.52 6.48
Example 1
A student measures the melting point of a sample
of beryllium and does four trials. The trials
result in melting points of 1267 oC, 1245 oC,
1270 oC, 1255 oC. Calculate the range and
comment on precision. Also calculate the
percent error (accepted = 1278 oC.)
Error Analysis: Range
Example 2
A student measures the density of a sample of
lead and does four trials. The trials result in
densities of 11.3, 10.5, 11.9, 10.8 g/cm3. The
accepted density of lead is 11.4 g/cm3.
Comment on accuracy and precision.
Scientific Method
A. Hypothesis
– untested, educated guess
B. Theory – successfully tested hypothesis
C. Law – Theory with NO known exceptions
Hypothesis
Theory
Law
Control Vs. Experimental
Groups
• Control – Nothing happens to
• Experimental – Change ONE variable
Example: Plant growth
Control
Experimental
16a) 1.5 X 1011 m b) 150 Gm
32a) 0.10 nm
c) 1.0 X 1010 A
b) 1.0 X 105 fm
d) 9.5 X 1025 A
42a) 1.00 X 109 cm3
c) 6.10 X 107 in3
b) 3.53 X 104 ft3