Transcript Document

Conversion Factors
and
Unit Cancellation
A physical quantity must include:
Number + Unit
Some Prefixes
•
•
•
•
•
•
•
Kilo Hecto Deca Deci Centi Milli -
1000
100
10
1
0.1
0.01
0.001
k
h
da
d
c
m
Length
• The basic unit of length in the metric system is
the meter (m)
• Metric Units of Length
–
–
–
–
–
–
–
Kilometer (km) = 1000 m
Hectometer (hm) = 100 m
Decameter (dam) = 10 m
Meter (m) = 1 m
Decimeter (dm) = 0.1 m
Centimeter (cm) = 0.01 m
Millimeter (mm) = 0.001 m
Mass
• The basic unit of mass in the metric system is a
gram (g)
• 1 g = mass of water in a cube that measures 1
cm x 1 cm x 1cm
• Metric Units of Mass
–
–
–
–
–
–
–
Kilogram (kg) = 1000 g
Hectogram (hg) = 100 g
Decagram (dag) = 10 g
Gram (g) = 1 g
Decigram (dg) = 0.1 g
Centigram (cg) = 0.01 g
Milligram (mg) = 0.001 g
Capacity
• Liquid substances are measured in units of capacity.
• The basic unit of mass in the metric system is a liter (L)
• 1 L = capacity of a cube that measures 10 cm x 10 cm x
10 cm
• Metric Units of Capacity
–
–
–
–
–
–
–
Kiloliter (kL) = 1000 L
Hectoliter (hL) = 100 L
Decaliter (daL) = 10 L
Liter (L) = 1 L
Deciliter (dL) = 0.1 L
Centiliter (cL) = 0.01 L
Milliliter (mL) = 0.001 L
Volume
• The most commonly used
metric units for volume
are the liter (L) and the
milliliter (mL).
– A liter is a cube
1 decimeter (dm) long on
each side.
– A milliliter is a cube
1 centimeter (cm) long
on each side.
© 2012 Pearson
Education, Inc.
Ladder Method
1
2
KILO
1000
Units
3
HECTO
100
Units
DEKA
10
Units
DECI
0.1
Unit
Meters
Liters
Grams
How do you use the “ladder” method?
1st – Determine your starting point.
2nd – Count the “jumps” to your ending point.
3rd – Move the decimal the same number of
jumps in the same direction.
CENTI
0.01
Unit
MILLI
0.001
Unit
4 km = _________ m
Starting Point
Ending Point
How many jumps does it take?
4. __. __. __. = 4000 m
1
2
3
Conversion Practice
Try these conversions using the ladder method.
1000 mg = _______ g
1 L = _______ mL
160 cm = _______ mm
14 km = _______ m
109 g = _______ kg
250 m = _______ km
Compare using <, >, or =.
56 cm
6m
7g
698 mg
Metric Conversion Challenge
Write the correct abbreviation for each metric unit.
1) Kilogram _____
4) Milliliter _____
7) Kilometer _____
2) Meter _____
5) Millimeter _____
8) Centimeter _____
3) Gram _____
6) Liter _____
9) Milligram _____
Try these conversions, using the ladder method.
10) 2000 mg = _______ g
15) 5 L = _______ mL
20) 16 cm = _______ mm
11) 104 km = _______ m
16) 198 g = _______ kg
21) 2500 m = _______ km
12) 480 cm = _____ m
17) 75 mL = _____ L
22) 65 g = _____ mg
13) 5.6 kg = _____ g
18) 50 cm = _____ m
23) 6.3 cm = _____ mm
14) 8 mm = _____ cm
19) 5.6 m = _____ cm
24) 120 mg = _____ g
Compare using <, >, or =.
25) 63 cm
26) 536 cm
6m
53.6 dm
27) 5 g
28) 43 mg
508 mg
5g
29) 1,500 mL
30) 3.6 m
1.5 L
36 cm
Temperature
© 2012 Pearson Education, Inc.
Temperature
•
•
•
•
The kelvin is the SI unit of temperature.
It is based on the properties of gases.
There are no negative Kelvin temperatures.
K = C + 273.15
Temperature
• The Fahrenheit scale is not used in scientific
measurements.
• F = 1.8(C) + 32
Calculation Corner: Unit Conversion
1 Cal = 4.184 J
Calculation Corner: Unit Conversion
1 Cal
4.184 J
4.184 J
1 Cal
“Conversion factors”
Calculation Corner: Unit Conversion
1 Cal
4.184 J
4.184 J
1 Cal
“Conversion factors”
(
5 Cal
)(
4.184 J
1 Cal
)
=
20.92 J
How many cm are in 1.32 meters?
equality: 1 m = 100 cm
(or 0.01 m = 1 cm)
applicable conversion factors:
______
1m
100 cm
or
(
100 cm
______
1m
)
100 cm = 132 cm
X cm = 1.32 m ______
1m
We use the idea of unit cancellation
to decide upon which one of the two
conversion factors we choose.
How many meters is 8.72 cm?
equality: 1 m = 100 cm
applicable conversion factors:
______
1m
100 cm
or
(
100 cm
______
1m
)
1m
X m = 8.72 cm ______
= 0.0872 m
100 cm
Again, the units must cancel.
How many kilometers is
15,000 decimeters?
( )(
1m
X km = 15,000 dm ____
10 dm
)
1 km
______
= 1.5 km
1,000 m
How many seconds
is 4.38 days?
( )(
24 h
X s = 4.38 d ____
1d
)( )
60
min
_____
1h
60 s
____
1 min
= 378,432 s
If we are accounting for significant
figures, we would change this to…
3.78 x 105 s
Simple Math
with
Conversion Factors
Example Problem
Measured dimensions of a rectangle:
length (L) = 9.70 cm
width (W) = 4.25 cm
Find area of rectangle.
L
A=L.W
= (9.70 cm)(4.25 cm)
= 41.2
2.
cm cm
W
Convert 41.2 cm2 to m2.
(
)
1m
X m2 = 41.2 cm2 ______
= 0.412 m2
WRONG!
100 cm
= 0.412 cm.m
Recall that…
41.2 cm2 = 41.2 cm.cm
X m2 = 41.2 cm.cm
(
)(
)
1m
______
1m
______
100 cm
100 cm
= 0.00412 m2
X
m2
= 41.2
cm2
(
)
1m
______
100 cm
2
=
0.00412 m2
Convert 41.2 cm2 to mm2.
Recall that…
41.2 cm2 = 41.2 cm.cm
(
X mm2 = 41.2 cm.cm 10
mm
_____
1 cm
)(
1 cm
=
4,120 mm2
10
mm
_____
)
= 4,120 mm2
(
mm
_____
X mm2 = 41.2 cm2 10
1 cm
2
)
Measured dimensions of a rectangular solid:
Length = 15.2 cm
Width = 3.7 cm
Height = 8.6 cm
H
W
Find volume of solid.
L
V=L.W.H
= (15.2 cm)(3.7 cm)(8.6 cm)
3
= 480 cm
Convert to m3.
cm.cm.cm
(
)(
1m
X m3 = 480 cm32 _____
100 cm
1m
_____
)(
100 cm
)
1m
_____
=
100 cm
or
3
(
)
(
3
1m
X m3 = 480 cm3 _____
100 cm
0.000480 m3
=
or
X
m3
= 480
cm3
)
1m
_________
4.80 x 10-4 m3
=
1000000 cm3
Convert to m3...
Measured dimensions of a rectangular solid:
Length = 15.2 cm 0.152 m
Width = 3.7 cm 0.037 m
Height = 8.6 cm 0.086 m H
Find volume of solid.
W
L
V=L.W.H
= (0.152 m)(0.037 m)(0.086 m)
= 0.000480 m3
By what factor do mm and cm differ?
1 cm = 10 mm
10
By what factor do mm2 and cm2 differ?
1 cm
(1
cm)22==100
(10 mm
mm)2 2
100
By what factor do mm3 and cm3 differ?
1 cm
mm33
(1
cm)33==1000
(10 mm)
1,000
‫مايعات‬
‫چگالي‬
‫جيوه‬
‫‪13500‬‬
‫آب‬
‫‪1000‬‬
‫گازها‬
‫چگالي‬
‫نفت‬
‫‪800-950‬‬
‫دي اكسيد‬
‫‪2‬‬
‫‪920‬‬
‫كربن‬
‫‪810‬‬
‫اكسيژن‬
‫‪43/1‬‬
‫هــوا‬
‫‪29/1‬‬
‫هليوم‬
‫‪18/0‬‬
‫هيدروژن‬
‫‪09/0‬‬
‫هواي مايع‬
‫(‪oC)194-‬‬
‫ازت مايع‬
‫(‪oC-)196‬‬
‫الكل (تانون)‬
‫‪790‬‬
‫هليون مايع (‪-‬‬
‫‪125‬‬
‫‪)269‬‬
‫جامدها‬
‫پالتين‬
‫طال‬
‫سرب‬
‫نقره‬
‫مس‬
‫آهن (فوالد)‬
‫روي‬
‫چگالي‬
‫‪21400‬‬
‫‪19300‬‬
‫‪11300‬‬
‫‪10500‬‬
‫‪8930‬‬
‫‪7800‬‬
‫‪6900‬‬
‫جامدها‬
‫چوب‬
‫آلومينيوم‬
‫يخ‬
‫چگالي‬
‫‪250-1000‬‬
‫‪2700‬‬
‫‪920‬‬