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V. Units of Measurement
VI. Metric System
Quantity - number + unit
UNITS MATTER!!UNITS MATTER!!
Quantity Base Unit Abbrev.
Length
Mass
Time
Temp
meter
kilogram
second
kelvin
m
kg
s
K
Amount mole mol
Symbol
l
m
t
T
n
mega- M 1x106
deci- d 1x10-1
centi- c 1x10-2
milli- m 1x10-3
Prefix Symbol Factor
micro- 1x10-6
nano- n 1x10-9
kilo- k 1x103
BASE UNIT ---
457 dm = km
457 dm = mm
1) 20 cm = ______________ m
2) 0.032 L = ______________ mL
3) 45 km = ______________ dm
4) 805 cm = ______________ km
0.2
0.00805
450,000
32
VII. Dimensional Analysis
You will be using these converstions throughout the year, so its best to take the time to memorize them now.
1.00 in = 2.54 cm2.2 lbs = 1.00 kg1.1 qts = 1.00 L
metric from earlier table
Steps:
1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number hit enter.
4. Check units & answer.
3
3
cm
g
1
cm
In algebra In algebra abab What do we do?What do we do? b b
In scienceIn science called factor-label methodcalled factor-label method◦ Units, or “labels” are canceled, or “factored” out
g
Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?
Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?
8.0 cm 1 in
2.54 cm= 3.2 in
How many milliliters are in 1.00 quart of milk?
How many milliliters are in 1.00 quart of milk?
1.00 qt 1 L
1.057 qt= 946 mL
qt mL
1000 mL
1 L
Eastview football needs 550 cm for a 1st down. How many yards is this?
Eastview football needs 550 cm for a 1st down. How many yards is this?
550 cm 1 in
2.54 cm= 6.0 yd
cm yd
1 ft
12 in
1 yd
3 ft
A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?
A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?
1.3 m 100 cm
1 m= 86 pieces
m pieces
1 piece
1.5 cm
You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.
You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.
lb cm3
1.5 lb 1 kg
2.2 lb= 35 cm3
1000 g
1 kg
1 cm3
19.3 g
A favorite item at the fair is bacon on a stick. If each stick holds approximately 0.15kg of bacon and the booth serves an average of 45 people an hour, how many pounds of bacon are consumed in the 12 days of the fair? (The gates open at 6:00am and close at midnight.)
Use the conversion factors you already know, but when you square or cube the unit, don’t forget to cube the number also!
Best way: Square or cube the ENITRE conversion factor
Example: Convert 4.3 cm3 to mm3
4.3 cm4.3 cm33 (10 mm) (10 mm) 33
(1 cm)(1 cm) 3 3 = 4.3 cm4.3 cm33 10 1033 mm mm33
1 133 cm cm33
= 4300 mm3
1000 cm3 (1 dm)3
(10 cm)3 = 1 dm3
So, a dmSo, a dm33 is the same as a Liter ! is the same as a Liter !
A cmA cm33 is the same as a milliliter. is the same as a milliliter.
How many liters of water would fill a container that measures 75.0 in3?
How many liters of water would fill a container that measures 75.0 in3?
75.0 in3 (2.54 cm)3
(1 in)3= 1.23 L
in3 L
1 L
1000 cm3