|
Metric System
Dr. Robert J. Rapalje,
Retired
©
2002
Seminole State College of Florida
Tech Prep Integrations
NOTE:
For additional information on the metric system, please see also the website
of the U.S. Metric Association
(USMA),
Inc. , a non-profit, national
organization, founded in 1916 at
www.metric.org. Please feel free to contact
Paul Trusten,
R.Ph.,
Public Relations Director U.S. Metric Association (USMA),
Inc. (email:
trusten@grandecom.net
) about metric issues. They will be happy to
help you.
Return to main page
Math in Living
C
O
L O
R
!!
Since the beginning of commerce and trade, a standardized
system of measurements has been essential. To be effective, such systems, which
include measures of distance, volume, and weight, must be uniform, easy
to remember and work with, and widely accepted. Although the metric
system is widely used throughout the world today, we continue to make
considerable use the English system in the United States. In this section, we
will investigate the English and Metric Systems, how they were developed, and
how they work. If you are not familiar with the metric system, you will be
amazed at how easy it is to remember and how simple it is to use.
The English System and Early Systems of Measurement
The system of measurements that we know as the English system
did not come from England. Rather, it evolved over thousands of years from a
variety of cultures all around the world. The main problem with early systems of
measurement was lack of standardization, which was undoubtedly compounded by the
vanity and arrogance of kings who ruled with absolute authority instead of
compassion and common sense. Can you picture King Henry I of England, who
defined the yard as the distance from the tip of his nose to the tip of
his outstretched thumb?
Many early units of measure were named after and represent
body parts. For example, the cubit, which is used extensively in the Bible,
represented the length of the forearm or six handbreadths. But whose forearm is
the standard of measure? To make matters worse, there were several different
cubits. The Babylonian cubit, based upon the length of the forearm, ranged from
20.65 to 21.26 inches. The Egyptians, using six handbreadths, had two cubit
measures, the Common and the Royal, which ranged from 17.70 to 20.64. The
Hebrews also had two cubits, one of which was known as the common cubit and the
other, which was one full handbreadth longer than common cubit.
Many of the units of measure that are commonly used today
have an interesting history. Consider the foot. The question that certainly
arose was, "Whose foot should be used for the standard?" The obvious
answer was, "The king’s foot!" Since the king’s actual foot could
obviously not be used in the workplace, accurate representations of the king’s
foot were needed. [Note: do you think this is why we call these representations
"rulers"?] Several problems resulted from this. How accurate were
these representations? How could this "foot" be subdivided to measure
distances smaller than a foot? What happened to the "foot" when the
king died, especially when the new king decided that his foot should be
the new standard of measure for the foot? Can you imagine the problems that
arose in the world of business of that day among kingdoms far and near, using
the "feet" of different kings as their not-so-standard unit of
distance?
An early attempt to standardize these measurements was made
by the Romans who introduced the mile, the milia passuum. The
Romans defined the milia passuum to be 1000 double-steps (about 5000 feet) of
their marching legions, and so it remained for about 1000 years. But then the
English defined the acre to be the amount of land that a yoke of oxen could plow
in one day and the furlong to be the length of a furrow plowed across a square
10-acre field. They further agreed that a furlong would be 220 yards. But the
furlong did not divide evenly into the Roman mile, so Queen Elizabeth lengthened
the mile to an even 8 furlongs, which was established in 1593 by British
Parliament to be the statute mile (that is, 8 x 220 x 3 = 5280 feet in one
mile).
The following is a summary of measures from the English
system with abbreviations and conversion units.
English
System
Distance
Volume
Weight
Inch (in)
Teaspoon (tsp or t)
Ounce (oz)
Foot (ft)
Tablespoon (tbsp or T)
Pound (lb)
Yard (yd)
Ounce (oz)
Ton (T)
Rod (R)
Cup (c)
Furlong (fur)
Pint (pt)
Quart (qt)
Gallon (gal)
1 ft = 12 in
1 tbsp = 3 tsp
1 lb = 16 oz
1 yd = 3 ft = 36 in
1 oz = 2 tbsp = 6 tsp = 1/8 c
1 short ton
= 2000 lb
1 statute mi = 5280 ft
1 pt = 16 oz = 2 c
1 long ton = 2240
lb
1 nautical mi = 6079 ft
1 gal = 4 qt = 8 pt = 16 c = 96 oz
Notice that there is no consistency among the abbreviations
in the English system. As examples, notice that the abbreviation for
"inch" is the first two letters of the word, while the abbreviations
for "foot" and "yard" are the first and last letters of the
word. The abbreviations for "rod" and "ton" are only one
capital letter, while the abbreviations for "furlong" and
"gallon" consists of three lowercase letters. Finally, where did we
get abbreviations of "oz" for "ounce" and "lb" for
"pound"? (The answer to this question goes back to the latin words for
ounce and pound (libra).
Secondly, notice that there is no consistency among the
conversion numbers. There are 12 inches in a foot, 3 feet in a yard, 5280 feet
in a mile, unless it is a nautical mile, in which case there are 6079 feet. The
systems of volume and weight have equally meaningless conversion numbers. These
numbers are difficult to remember for anyone having to learn the system, and
extremely difficult to work with for everyone, even for those who are familiar
with the system. Finally, there seems to be no connection between distance,
volume, and weight in the English system, except that the unit of ounces is used
in both as a volume and weight.
Contrast this to the metric system!
The Metric System
The origin of the metric system stands in stark contrast to
that of the English system. Whereas the English system evolved
over time and cultures, the metric system, known also as System
Internationale (SI), was created systematically by French scientists
in the 1790’s during the Napoleonic reign. While the units of measure and
abbreviations in the English system are unrelated, the units and abbreviations
in the metric system are interrelated, systematic, and easy to remember. Best of
all, each conversion within the metric system is a power of 10.
The basic unit of distance in the metric system is the meter
(m), which is slightly more than a yard (approximately 39.37 inches). The
basic unit of volume is a liter (l), which is slightly more than a quart.
The basic unit of mass (comparable to what is used in the English system as a
measure of weight) is the gram (g). A gram is the approximate mass (or
weight) of a paper clip.
The
meter was defined by the French scientists to be
one ten-millionth of the distance from the equator to the North Pole. [Note: How
do you think they measured this? With a yardstick?] More precisely, the
meter is also defined in terms of light wavelengths. Specifically, the meter is
defined to be 1,670,763.73 wavelengths of a spectral yellow light emitted by
Krypton gas.
To measure distances smaller than a
meter, the
meter is
subdivided into smaller units: tenths of a meter (decimeter), hundredths
of a meter (centimeter), thousandths of a meter (millimeter),
millionths of a meter (micrometer), etc. Distances larger than a meter
are measured in units that are 10 meters (decameter), 100 meters (hectometer),
1000 meters (kilometer), 1,000,000 meters (Megameter) etc.
Altogether, there are several dozen such prefixes for even larger and smaller
measurements, but for business and scientific purposes it is sufficient to list
the main ones here. The prefixes, their abbreviations, and values are summarized
on the following metric line. For your convenience, I have
highlighted and color-coded the most frequently used units:
--------●-------●-------●------●--------●--------●----------●-----------●---------●--------●-------●--------●-------●------
Prefix: Mega Kilo Hecto Deca
Basic Unit Deci
Centi
Milli
Micro
Abbrev:
M
k
h dc
m, l, g
d
c
m
mc or μ
Value: 1,000,000
1,000
100
10
1
1/10
1/100
1/1,000
1/1,000,000
When
measuring volumes in the metric system, the
liter
is the basic
unit of
measure. To measure volumes that are more or less than a
liter,
larger or smaller units are created in exactly the same way as for the
meter:
1,000,000 liters (Megaliter), 1000 liters (kiloliter), 100 liters
(hectoliter), 10 liters (decaliter), tenths of a liter (deciliter),
hundredths of a liter (centiliter), thousandths of a liter (milliliter),
millionths of a liter (microliter), etc.
The
basic unit
of mass (weight) in the metric system is the
gram. When measuring masses (weights) that are larger or smaller than a
gram,
larger or smaller units are likewise created: 1,000,000 grams (Megagram),
1000 grams (kilogram), 100 grams (hectogram), 10 grams (decagram),
tenths of a gram (decigram), hundredths of a gram (centigram),
thousandths of a gram (milligram), millionths of a gram (microgram),
etc.
At the time
that I first wrote this page years ago, the prefix units of
Mega seemed
LARGE enough and micro seemed SMALL enough for most normal
applications of that day. At that time I remember being excited to boast that my
"new" computer that had 2 megabites of memory on the hard drive! Wow!!
This was a LOT of memory in the early 1990s!
There were then and are today units that are larger than
Mega
and smaller than micro, but such large
or small units were hardly needed on
a daily basis years ago. However, they ARE used today! If the prefix
Mega
represents 1,000,000 (million), then Giga represents billion--that is, 1000 Megas, or 1,000,000,000
units. If
micro represents 1/1,000,000 (one
millionth), then nano
represents 1/1,000,000,000 (one billionth).
For a more
extensive list of prefixes see an outstanding website by Gordon Speer, click
here.
When using such
extremely large (or small) numbers, it may be helpful to use scientific
notation. Keeping it simple,
1,000 = 103
Thousand Kilo k
1,000,000 = 106
Million Mega M
1,000,000,000 =
109 Billion Giga G
0.001 = 10-3
thousandth milli m
0.000,001 = 10-6
millionth micro mc (medical) or μ (Greek
letter “mu”)
0.000,000,001 =
10-9 billionth nano n
For a more
detailed explanation of scientific notation, see my own explanation of this
topic by clicking
here.
Not only are the units of distance, volume, and consistent
within the metric system, they are also interrelated. Unlike the English system,
where there is no connection between units such as inches/feet and
pints/gallons, there is a connection between meters, liters, and grams.
Remember that the basic unit of distance in the metric system is the meter.
Imagine a cubic meter (that is, a cube whose sides are each one meter), filled
with water at 4° C.
Such a large cube filled with water will be extremely heavy,
take a cube that is one-tenth of a meter or one decimeter (see upper right
corner in the cube) on each side, filled with liquid. This cubic decimeter
represents a volume of one liter.
Now, take one tenth of each side of the cubic decimeter (the
smallest cube pictured). Since one tenth of one tenth is one one-hundredth (centi-),
this forms a cubic centimeter. The mass (weight) of this cubic centimeter
is one gram and its volume is one milliliter.
Converting Within the Metric System
To convert measurements within the metric system is a simple
matter of multiplying or dividing by 10, 100, 1000, etc. Even simpler, it is a
matter of moving the decimal point to the left or right. The first step is to
draw a "metric line" with the basic unit in the center, marking off
six units to the left and six units to the right. (Note: unless Mega and micro
are needed, the basic unit and three units to the left and right will be
enough.)
--------●-------●-------●------●--------●--------●----------●-----------●---------●--------●-------●--------●-------●------
Prefix: Mega Kilo Hecto Deca
Basic Unit Deci
Centi
Milli
Micro
Abbrev:
M
k
h dc
m, l, g
d
c
m
mc or μ
To convert from one unit to another simply count the number of places to the
left or right, and move the decimal in that direction that many places.
Example 1: Convert
a) 6.5 m = _________ cm
b) 6.5 l = _________ cl
c) 6.5 g = _________ cg
Solution: In each part of this example, you are
converting from the the basic unit "m," "l," or
"g" to a unit with prefix "c" for "centi."
Each of these is a move of two spaces to the right, so in
each part, you must move the decimal two places to the right. They are
essentially the same problem!
a) 6.5 m = 650 cm
b) 6.5 l = 650 cl
c) 6.5 g = 650 cg
Example 2: Convert
a) 6.5 cm = _________mm
b) 6.5 ml = _________l
c) 6.5 g = _________kg
d) 6.5 mg = _________ mcg
Solution:
a) You are converting from the prefix
"c" for centi to "m" for milli, which is one space
to the right. You must move the decimal one place to the right: 6.5 cm =
65 mm.
b) You are converting from the prefix "m"
for "milli" to the basic unit "l," which is three
spaces to the left. You must move the decimal three places to the left:
6.5 ml = 0.0065 l.
c) You are converting from the basic unit
"g" to "k" for "kilo", which is three
places to the left. You must move the decimal three places to the left:
6.5 g = 0.0065 kg.
d) You are converting from "m" for "milli"
to "mc" for "micro", which is three places to the
right. You must move the decimal three places to the right: 6.5 mg = 6,500
mcg.
|----------|----------|---------|-----------|-----------|-----------|
k
h
dc basic unit d
c m
m, l, g
Example 3: Convert
a) 0.054 m =
_________m
b) 780 kl = _________l
c) 60 mg = _________kg
Solution:
a) You are converting from the basic unit "m" to
milli "m," which is three spaces to the right. You must move
the decimal three places to the right: 0.054 m = 54 mm.
b) You are converting from the prefix "k" for
"kilo" to the basic unit "l," which is three spaces
to the left. You must move the decimal three places to the left: 780 kl
= 780,000 l.
c) You are converting from the milli "m" to "k"
for "kilo", which is six places to the left. You must move the
decimal six places to the left: 60 mg = 0.00006 kg.
Example 4: A woman is running the 5 k race (which means
"kilometers") to raise money for the American Cancer Society. If
the steps that she takes in the race are approximately one meter in
length, approximately how many steps does she take in running the race?
Solution: Convert 5 km = ________ m
Move the decimal three places to the right.
Answer = 5000 m. or approximately
5000 steps.
Example 5: In a canned goods drive for Feed the
Hungry, 300 people collect an average of 25 cans of food per person,
which average 305 grams per can. Approximately how many kilograms of
food were collected in the drive?
Solution: Multiply 300 x 25 x 305 = 2287500 grams
Now, convert 2287500 g = ____________kg.
Move the decimal three places to the left.
Answer =
2,287.5 kg.
Example 6: A swimming pool at the YMCA is has a
volume of 7500 cubic meters. How many liters of water are in the pool?
Solution: Each cubic meter of water contains 10 x 10 x 10 or
1000 liters of water.
There are therefore 7500 x 1000 or 7,500,000 liters of
water.
English to Metric Conversions and Metric to English Conversions
1 inch = 2.54 centimeters
1 centimeter = 0.3937 inches
1 foot = 0.3048 meter
1 meter = 39.37 inches
1 mile = 1.6093 kilometers
1 kilometer = 0.62137 mile
1 quart = 0.9464 liter
1 liter = 1.0567 quarts
1 gallon = 3.785 liters
1 liter = 0.2642 gallon
1 ounce = 28.35 grams
1 gram = 0.03527 ounce
1 pound = 0.4536 kilograms
1 kilogram = 2.2046 pounds
The key to converting from the English to metric or metric to
English system is to know the conversion numbers from the system you are given
to the system to which you are converting. If you have that conversion number,
then you can always multiply. The examples that follow will illustrate. Keep in
mind that these conversion numbers are NOT exact, and when they are used, a
round-off error is inevitable.
Example 7: Convert
a) 500 ft. = _________m.
b) 500 mi. = _________km.
c) 500 gal. = _________l.
d) 500 lb. = _________kg.
Solution: In each part of this example, you are converting English
system to metric system. Conveniently, each of the conversion numbers are
given above.
a) Multiply 500 ft x 0.3048 =
152.4 meters.
b) Multiply 500 mi x 1.6093 =
804.65 kilometers.
c) Multiply 500 gal x 3.785 =
1892.5 liters.
d) Mulitply 500 lb x .4536 =
226.8 kilograms.
Example 8: Convert
a) 3500 m. = _________in.
b) 40 km. = _________mi.
c) 2000 l. = _________qt.
d) 3500 g. = _________oz.
Solution: In each part of this example, you are converting English
system to metric system. Conveniently, each of the conversion numbers are
given above.
a) Multiply 3500 m x 39.37 =
137795 inches.
b) Multiply 40 km x 0.62137 = 24.9268 miles (round to 24.93 miles).
c) Multiply 2000 l x 1.0567 =
2113.4 quarts.
d) Multiply 3500 g x 0.03527 =
123.445 ounces.
In the previous examples, the conversion numbers were
conveniently given. What must be done if the necessary conversion numbers are
NOT given? Answer: Convert what you have to the other system in the most
convenient way, then convert to the appropriate unit. When converting within a
given system, remember that when you are converting from larger to smaller units
(like feet to inches), you multiply by the conversion number (like multiply
times 12). When converting from a smaller to larger units (like inches to feet),
you divide by the conversion number (like divide by 12). Also remember that the
results are NOT exact, and using different methods will frequently result in
different round-off errors.
Example 9: Convert 3500 m. = _________ft.
Solution: First convert from meters to inches, then from inches to feet.
3500 m x 39.37 = 137795 inches.
To convert from inches to feet, you must divide by 12.
137795 inches ∕ 12 = 11,482.92 feet or approximately 11,500
feet.
Example 10: Convert 3500 mi. = _________m.
Solution: First convert from miles to km, then from km to meters.
3500 mi x 1.6093 = 5632.55 km.
To convert from km to meters, move the decimal 3 places to right.
5632.55 km = 5,632,550 m. (approximately)
- OR - First convert from miles to feet, then from feet to meters.
3500 mi x 5280 = 18,480,000 ft.
18,480,000 ft x 0.3048 = 5,632,704 m. (approximately)
[Note: The difference in these two answers highlights the
fact that if the conversion numbers are only accurate to four digits, then
the answers also are only accurate to four digits. We can conclude that the
answer is approximately 5,633,000 m.]
Example 11: Convert 20 kl. = _________gal.
Solution: First convert from kl to liters, then from liters to
gallons.
20 kl = 20,000 liters.
20,000 l. x 0.2642 = 5284 gallons. (approximately)
Example 12: Convert 35 ml. = _________oz.
Solution: First convert from ml. to liters, then from liters to quarts,
from quarts to pints, and finally from pints to ounces. (There must be a
better way!)
35 ml = 0.035 liters
0.035 liters x 1.0567 = 0.0369845 quarts
0.0369845 quarts x 2 = 0.073969 pints x 16 = 1.183504 or 1.18 ml.
Example 13: The woman (see Example 4) who is running
the 5 k race to raise money for the American Cancer Society is wondering
how far is the run in miles. Express the distance of the 5 k race in
miles.
Solution: Convert 5 km = ________ mi.
5 km. x 0.62137 = 3.10685 miles.
Answer = approximately 3.1 miles.
Example 14: In order to finish in the top three of a
5 k race (see previous exercise), a woman needs to run a 7-minute mile.
If she maintains this pace consistently throughout the race, how long
will it take her to finish, and how long will it take her to run each
kilometer of the race?
Solution: From the previous exercise, the race is 3.1
miles. If it takes 7 minutes to run 1 mile, this will take 3.1 x 7 or 21.7
minutes to run 3.1 miles, which is equivalent to 5 kilometers. Now,
divide 21.7 minutes (total time) by 5 kilometers, which is 4.034 minutes
per kilometer. To maintain this pace, she should run about 4 minutes
per kilometer.
Example 15: Because of a drought in Africa, Feed the
Hungry needs to provide food for 225,000 people for six months. If each
person to be fed needs 500 grams of food per day in order to survive,
how many kilograms of food must be collected to meet this need? How many
tons of food is this? (Assume 30 days per month.)
Solution: Six months is 180 days. Multiply 225,000 x
180 x 500 grams. Because this number is so large, it may be easier to
calculate this in kilograms. As you recall, to convert from 500 grams
(basic unit) to kilograms, move the decimal three places to the left,
which is 0.500 or 0.5 kg.
225,000 x 180 x 0.5 kilograms =
20,250,000 kg.
Now, to convert to tons, you must first change
kilograms to pounds. Since 1 kg = 2.2046 lb, multiply 2.2046 x
20,250,000 = 44,643,150 lb. Since 1 ton is 2000 pounds, and you are
converting from smaller to larger units, you must divide by 2000. The
answer is 44,643,150/ 2000, which is 22,321.75 tons.
Example 16: The competition pool at the YMCA in
Orlando, FL. is 25 yards by 50 meters, and it has a depth of 7 feet. How
many liters of water are in the pool?
Solution: It is necessary first to convert the
dimensions of yards to feet and then the feet to meters. Question: How
many feet are in a yard? Answer: It depends upon how many people are in
the yard! Really, there are 3 feet in a yard, so 25 yards equals 75
feet. Since 1 foot = 0.3048 feet, 75 feet = 75 x 0.3048 = 22.86 meters,
and 7 x 0.3048 = 2.1336 meters. The total volume of the pool is V=LWH,
which is 50 x 22.86 x 2.1336 = 2438.70 cubic meters. As in Example 6,
each cubic meter contains 1000 liters, so the pool contains about 2,438,700
liters of water.
Example 17: Because of evaporation and splashing of
water, water level in the competition pool at the YMCA (see Example 16)
is down by 3 inches. Remembering that the pool is 25 yards by 50 meters
and 7 feet, how many liters of water will be needed to refill the pool?
Solution: The volume of water to be replaced is 25
yards by 50 meters by 3 inches. Again, it is necessary first to convert
all of the dimensions to meters. Of course, 3 inches (divide by 12) is
0.25 feet, and 25 yards is 75 feet. Using 1 foot = 0.3048 feet, 0.25
feet = 0.25 x .3048 = 0.0762 meters, and 75 x 0.3048 = 22.86 meters. The
total volume to be replaced is V=LWH, which is 50 x 22.86 x 0.0762 =
87.0966 cubic meters. Since each cubic meter contains 1000 liters, it
will take about 87,097 liters to refill the pool.
Medical Applications—Dosages
Example 18:
a) How many milliliters are in one ounce?
b) How many milliliters are in one tablespoon?
c) How many milliliters are in one teaspoon?
Solution:
a) Beginning with 1 quart = 0.9464 liter,
remember that there are 16 ounces in a pint and 2 pints in a quart.
Therefore, 1 quart is 32 ounces, so
1 ounce = 1/32 quart x 0.9464 = 0.029575 liters.
To convert liters to milliliters, move the decimal 3
places to the right:
1 ounce = 29.575 milliliters.
b) 2 tablespoons =1 ounce = 29.575 milliliters, so
divide by 2:
1 tablespoon = 14.7875, round off to 15 milliliters.
c) 3 teaspoons = 1 tablespoon = 14.7875 milliliters, so
divide by 3:
1 teaspoon = 4. 929 milliliters, round off to 5
milliliters.
Example 19: According to a very old cold remedy, two
tablespoons of medicine were to be administered three times a day. Express
this dosage in milliliters, and determine how many milliliters would be
administered in one week.
Solution: 2 tablespoons equals 1 ounce, which is 29.575
milliliters.
Three dosages per day for a week will be 21 dosages per
week.
29.575 x 21 = 621.075 milliliters per week.
Example 20: A 1.5-milliliter injection is to be
administered three times a day using a 3-milliliter syringe. The
medication comes in 10-milliliter vials. How many syringes and how many
vials will be needed in a week?
Solution: At three injections per day, a total of 21
syringes will be needed. Now, multiply 21 x 1.5 milliliters = 31.5
milliliters. Finally, since the medication comes in 10-milliliter vials,
divide by 10, which is 3.15 vials. This will require 4 vials.
(Note: the size of the syringe was not needed.)
Example 21: A 2.5-milliliter injection is to be
administered three times a day using a 3-milliliter syringe. The
medication comes in 10-milliliter vials. How many syringes and how many
vials will be needed in 6 months (assume a 30 day month)?
Solution: At three injections per day, a total of 3
x 30 x 6 = 540 injections, so 540 syringes will be needed. Now,
multiply 540 x 2.5 milliliters = 1350 milliliters. Finally, since the
medication comes in 10-milliliter vials, divide by 10, which is 135
vials.
Example 22: At a certain hospital, on the average, 120
patients are administered injections of six milliliters of a certain
medicine, four times a day. How many liters of the medication will be
needed by the hospital in a 30-day month?
Solution: 6 milliliters x 4 x 30 x 120 = 86,400
milliliters.
To convert to liters, move the decimal 3 places to the
left.
86,400 milliliters =
86.4 liters.
Remember that metric units in grams (g) measure
the weight (technically, the mass) of a substance, while the units liters (l)
, milliliters (ml), and cubic centimeters (cc) measure the volume of
the substance. Under normal circumstances, a volume of 1 milliliter is
the same as 1 cubic centimeter. Moreover, the weight of a milliliter
(or cubic centimeter) is 1 gram.
EXERCISES
1. Give the names and abbreviations of the metric units on the following
"metric line."
1,000,000
1,000 100 10
Basic 1/10 1/100
1/1000 1/1,000,000
|-------|-------|-------|--------|--------|--------|---------|---------|--------|-------|-------|-------|
Name _____
_____ _____ _____ ______ _____
_____ _____
_____
Abbrev _____
_____ _____ _____ ______ _____
_____ _____
_____
2. Convert each of the following metric to metric units.
a) 1 m. = ____________ cm.
f) 0.05 dg. = ____________kg.
b) 1 l. = ____________ kl.
g) 4000 hl. = ____________ l.
c) 50 cg. = ____________ mg.
h) 4000 g. = _____________Mg.
d) 50 cm. = ____________ km.
i) 37.5 ml. = ____________mcl.
e) 0.05 kg =____________ dg.
j) 37.5 dg = ____________ mg.
In 3 – 13, use the following to convert metric to English or English to
metric units.
1 cm = 0.39 in
1 in = 2.54 cm
1 m = 39.37 in
1 ft = 0.3048 m
1 km = 0.62 mi
1 mi = 1.6 km
1 liter = 1.06 qt
1 qt = 0.946 liter
1 kg = 2.2 lb
1 lb = 0.45 kg
1 gram = 0.035 oz
1 oz = 28.35 grams
3. a) 4 mi. = __________ km.
f) 6000 kg. = __________tons.
b) 4 km. = __________ mi.
g) 600 liters = __________gal.
c) 25 lb. = __________ kg.
h) 500 gal. = __________liters
d) 25 kg. = __________ lb.
i) 50 oz = __________ mg.
e) 700 lb. = __________ g.
j) 650 ml = __________ qt.
4. a) 2.5 Ml. = ____________ gal.
d) 0.075 in. = ____________ mcm.
b) 0.005 oz. = ____________ mcg.
e) 35000 mcl = ____________ pints
c) 0.005 ft. = ____________ cm.
f) 340 Tons = ____________Mg.
In 5 – 8, convert the units as indicated. Explain accuracy
limitations and discrepancies in your answers.
5. Convert 4000 inches to meters by converting:
a) from inches to centimeters,
b) from inches to feet, then from
centimeters to meters. then from feet to meters.
6. Convert 7.5 kilometers to feet by converting:
a) from kilometers to meters,
b) from kilometers to miles,
from meters to inches, then from miles to
feet, then from inches to feet.
7. Convert 3000 meters to feet by converting:
a) from meters to kilometers,
b) from meters to inches,
from kilometers to miles, then from inches to feet.then from miles to feet.
8. Convert 5000 grams to pounds by converting:
a) from grams to kilograms,
b) from grams to ounces,
then from kilograms to pounds. then from ounces to pounds.
5-8 Recap. In Exercises 5-8, what can be done if more accuracy is needed?
9. A man signs up to run a 25 k (kilometer) race to raise money for the
American Heart Association. Express this distance in miles.
10. If the man in the previous exercise runs a 6-minute mile consistently
throughout the race, what will be the average time for each kilometer, and how
long will it take him to run the race?
11. Compassion International is collecting food for 150,000 refugees in the
Sudan. If there is a need to provide 600 grams of food per person for two
months (30 days per month), how many kilograms of food will be needed? Express
this amount in tons of food.
12. a) How many gallons of water will it take to fill a kiloliter
container?
b) How much does this container of water weigh in kilograms?
c) How much does the container weigh in pounds?
13. Water is to be stored for hurricane relief in 55-gallon cylindrical
drums. How many of these drums would be needed to store 300 kiloliters of
water?
14. You just came home from the pharmacy with a prescription of antibiotic
for your child. On the bottle, the instructions are given to administer
"15 ml, three times per day." What does this mean in the English
system?
15. A 2-milliliter injection of a medication is to be administered three
times per day for 30 days. How many milliliters of the medication will be
needed? If the medication is dispensed in 10-milliliter vials, how many vials
will be needed?
16. A patient takes 300 mg of a medication twice per day for six weeks. How
many grams will be needed?
17. A hospital estimates that, on the average, 300 patients will be
administered injections of five milliliters of a particular medicine, three
times a day. Approximately how many liters of this medication will the
hospital use in a 360-day year?
18. Written on a toilet in the restroom of Company T is the following:
"6.0 Lpf/1.6 gpf." What is the meaning of this? Verify its accuracy.
ANSWERS TO EXERCISES
1.
1,000,000
1,000 100 10 Basic
1/10 1/100 1/1000
1/1,000,000
|------|-------|-------|--------|--------|-------|--------|--------|-------|------|------|------|
Name: Mega
Kilo Hecto Deca Meter Deci Centi
Milli
Micro
Liter
Gram
Abbrev: M
k h
dc m, l, g d
c m
mc or μ
2a) 100; b) 0.001; c) 500; d) 0.005; e) 500; f) 0.000005; g)
400000; h) 0.004; i) 37500; j) 3750.
3a) 6.4; b) 2.48; c) 11.25; d) 55; e) 315000; f) 6.6; g) 159;
h) 1992; i) 1417500; j) 0.689.
4a) 662500; b) 141750; c) 0.1524; d) 1905; e) 0.0742; f) 306.
5a) 101.6; b) 101.6; Appears to be accurate to four decimal places.
6a) 24,606.25; b) 24,552; Appears to be accurate only to three decimal
places, approx.=24,600.
7a) 9820.8; b) 9842.5; Appears to be accurate only to two decimal places,
approx.=9800.
8a) 11; b) 10.9375. Appears to be accurate only to two decimal places,
approx.=11.
Recap: If more accuracy is needed, then a more accurate value of the
conversion numbers must be used (see page 7).
9. 15.5 mi.
10. 3.72 min per km; 93 minutes total.
11. 5,400,000 kg; 5940 tons.
12a) 265 gal; b) 1000 kg; c) 2200 lb,
13. 1445.45 drums.
14. Approximately 1 tablespoon (or 3 teaspoons)
15. 12 vials.
16. 25.2 grams.
17. 1620 liters.
18. 6.0 Liters per flush/ 1.6 gallons per flush
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