Transcript Metric conversions! - Mr. Hounslow's Physics Page

Metric
Conversions!
Through dimensional analysis.
The Metric System
Uses SI units (Système
International d’Unités)
Universal standard of
measurement used in
science, and most of the
ENGLISH SYSTEM
Ounces, Pounds and Pints
8 ounces make a cup,
2 cups make a pint,
2 pints make a quart,
4 quarts make a gallon.
A pint of water weighs a pound.
An American barrel of dry measure is 105 dry quarts (116 liters), but a liquid barrel is 31.5
gallons (liquid) or 119 liters, unless the barrel contains petroleum, in which case it
contains 42 (US) gallons or 159 liters.
The three different ounces:
a fluid ounce is 29.573 ml
a troy ounce is 31.1 g
an ounce avoirdupois is 28.35 g
There's also something called "dry measure" with units of pint, quart, peck and bushel for
measuring quantities of fruits, grains, and whatnot. 1 pint dry is 0.551 l, while 1 pint
liquid is 0.473 l. Inches, Rods, Chains and Furlongs
An inch is the outer part of a man's thumb, 25.4 millimeter to be exact.
12 inches to a foot,
2 feet to a cubit or 3 feet to a yard.
A rod/pole is 5.5 yards (16.5 feet): The size of a big stick carried around by builders
Number Economy
Choose the correct
measurement for the job.
Instead of saying an object
traveled 5,000 meters you
can reduce that to 5
kilometers
n
1000
8
1000
7
1000
6
1000
5
1000
4
1000
3
1000
2
1000
1
n
10
24
10
21
10
18
10
15
10
12
10
9
10
6
10
3
1000
10
-
10
-
10
2
1
0
0
1000
10
-
10
-
10
−1
−2
−1
1000
−2
1000
−3
1000
−4
1000
−5
1000
−6
1000
−7
1000
−8
1000
−3
10
−6
10
−9
10
−12
10
−15
10
−18
10
−21
10
−24
10
Prefix
Symbol
Short scale
Long scale
Decimal equivalent in SI writing style
yotta
Y
Septillion
Quadrillion
1 000 000 000 000 000 000 000 000
zetta
Z
Sextillion
Trilliard (thousand trillion)
1 000 000 000 000 000 000 000
exa
E
Quintillion
Trillion
1 000 000 000 000 000 000
peta
P
Quadrillion
Billiard (thousand billion)
1 000 000 000 000 000
tera
T
Trillion
Billion
1 000 000 000 000
giga
G
Billion
Milliard (thousand million)
1 000 000 000
mega
M
Million
kilo
k
Thousand
hecto
h
Hundred
100
deca, deka
da
Ten
10
(none)
(none)
One
1
deci
d
Tenth
0.1
centi
c
Hundredth
0.01
milli
m
Thousandth
0.001
micro
µ (u)
nano
n
Billionth
Milliardth
0.000 000 001
pico
p
Trillionth
Billionth
0.000 000 000 001
femto
f
Quadrillionth
Billiardth
0.000 000 000 000 001
atto
a
Quintillionth
Trillionth
0.000 000 000 000 000 001
zepto
z
Sextillionth
Trilliardth
0.000 000 000 000 000 000 001
yocto
y
Septillionth
Quadrillionth
0.000 000 000 000 000 000 000 001
Millionth
1 000 000
1 000
0.000 001
Measuring Instruments
Time
Temperature
Distance
Mass
Volume
Second (s)
Celcius (oC),
Kelvin (K)
Meter (m)
Gram (g)
Liter (L),
3
Conversion Factors
Conversion
9
10
Large factor
106
units 103
102
101
Base
(L,m,g,s)
=
units
(L,m,g,s) =
(L,m,g,s) =
(L,m,g,s) =
(L,m,g,s) =
Base units (L, m, g, s)
Small
units
Prefix
1 giga (G)
1 mega (M)
1 kilo (k)
1 hecto (h)
1 deca (da)
NEED TO
MEMORIZE
Base
Conversion
Prefix
1
1units
(L,m,g,s) =
10
deci (d)
factor
1 (L,m,g,s) =
102
centi (c)
1 (L,m,g,s) =
103
milli (m)
1 (L,m,g,s) =
106
micro (μ)
1 (L,m,g,s) =
109
nano (n)
1 (L,m,g,s) =
1012
pico (p)
CONVERSION STEPS
Problem: convert 2.43 meters (m) into millimeters (mm)
STEP 1: Draw your table
STEP 2: Put given number and
2.43 m
unit over 1NO NAKED NUMBERS!!! EVERY
1
NUMBER NEEDS A UNIT!!! NO
UNIT = WRONG ANSWER!!!
STEP 3: Put given unit downstairs to
2.43 m
cancel
1
m
STEP 4: Put the unit you are looking for
mm
2.43
m
on top
m
1
STEP 5: Put a 1 in front of larger unit:
consult
!
2.43 m your chartmm
1
1
m
THIS IS THE MOST
IMPORTANT AND
MISSED STEP
STEP 6: LOOK UP THE PREFIX FOR
CONVERSION FACTOR
103 mm
2.43 m
milli = 1000 or 103
1
1
m
STEP 7: MULTIPLY ACROSS, NOT CROSS
MULTIPLY
2.43 E3
103 mm
2.43
m
1
1 m
=
1
mm
STEP 8: Reduce and double check your
unit
2.43 E3
=
1
2.43
E3
mm
Problem: Convert 561 liters (L) into kiloliters (kL)
561 L
1
1
kL
103
L
=
561 kL
5.61
kilo = 1000 or 103
103
E-1
kL
Problem: Convert 4.39 E4 seconds (s) into nanoseconds (ns)
4.39 E4 s
109 ns
1
1 s
=
4.39 E13 ns9
nano = 10
1
4.39
E13 ns
Problem: Convert 93561 grams (g) into Megagrams (Mg)
93561 g
1
Mg
1
106
g
=
93561 Mg 6
Mega = 10
106
9.36
E-2 Mg
PRACTICE
1. 3.45 Ms to s
2.1000 m to hm
3.356 L to pL
7
4.1.54 x 10 g to Gg
2 Stage Problems
You have to convert to the base
(L, m, g, s)
unit first
How do you know?
Problem has 2 prefixes and no
base unit alone
Convert to
Convert to
Convert to
m first
first
L first
Example: km
to cm, gMg
to mg,
2.55 km to cm
2.55 km
1
103 m
1 km
2.55 x 103 x 102 cm
1 x 1x 1
102 cm
1
m
=
=
2.55 x 105 cm
1.63 E3 cg to Mg
1.63E3 cg
1
1 g
102 cg
1.63E3 Mg
1 x 102 x 106
1 Mg
=
106 g
=
1.63 x 10-5 Mg
PRACTICE
1. 3.45 Ms to ms
2. 1000 nm to hm
3. 356 mL to pL
7
4. 1.54 x 10 cg to Gg
Answers: 1-5 table conversion
6.91m
1
9.10 E12m
1
1.8932 E6mm
1
100 cm
6.91
E2cm
9.10
E3 Gm
1.89
E3 m
1m
1 Gm
9
10
m
1m
3
10
mm
231 cm
1
94 km
1
1m
2
10
cm
103 m
1 km
2.31 m
9.40
E4 m
A
C
1m
1m
1km
100cm
3
10 mm
3
10 m
G
1Gm
9
10 m
I
E
K
9
10 nm
1Mm
1m
6
10 m
F
D
B
3
10 m
3
10 mm
100cm
1km
1m
1m
L
J
H
6
10 m
1m
9
10 m
1Mm
9
10 nm
1Gm
Meter Stick
1 meter
10
1
1
1
1
1
1
1
1
1
1
decimeter
decimeter
decimeter
decimeter
decimeter
decimeter
decimeter
decimeter
decimeter
decimeter
10
1
1
1
1
1
1
1 decimeter
centimeter
centimeter centimeter centimeter centimeter centimeter
1
1
1
1
centimeter centimeter centimeter centimeter
10
1
1
1
1
millimeter
millimeter
millimeter
millimeter
1
1
1
1millimeter
centimeter
millimeter millimeter
1
1
1
millimeter
millimeter
millimeter
Fractions : Ratios
Q: How do you convert a number
into a fraction?
Ex: 2.57
1
A: Put the number over 1!