 Objective:
Systems and Tools
In this lesson you will demonstrate your understanding
of the appropriate uses of standard units of measurement
and the relationships among units within the U.S. system
and within the metric system. You will also select and
use units and tools that will provide an appropriate
degree of precision.
If you need to check a word's definition, please go to the glossary by clicking the Vocabulary button
-
Attribute
-
Area
-
Perimeter
-
Volume
- Approximation
- Accurate
- Standard unit of measurement
Tips to
Remember:
Estimating
When you are asked to estimate,
be sure to solve the problem by estimating, not by
computing the answer and then rounding. Work the entire
problem by estimating without any actual computing
of the solution. You may not receive full credit for
your answer if compute then using that answer to estimate. |
Label Units
As you work with measurement,
always be sure to determine what units are in your
answer and then label your answer such. For example,
don't say that the area of the rectangle is 20. You
want to be sure to include the units of measure as
well. So the area of the rectangle would be 20 squared
feet. Remember if you are finding area, the units
are squared and if you are finding volume, the units
are cubed. |
Changing Units Within the Metric System
Here is how you use multiplying
by 10 to change a given metric measure to a smaller
unit.
Meters (x10) -- Decimeters (x10)
-- Centimeters (x10) -- Millimeters
For example:
1.35 meters (x10) =
13.5 decimeters (x10) =
135 centimeters (x10) =
1350 millimeters
Here is how you use division by 10 to change a
given measure to a larger unit.
Millimeters (divide
by 10) -- Centimeters (divide by 10) -- Decimeters
(divide by 10) -- Meters
For example:
768 millimeters (divide by 10) =
76.8 centimeters (divide by 10) =
7.68 decimeters (divide by 10) = .768 meters
|
Units of Length, Time, Weight, and
Volume
|
Units
of Length
|
| 1
foot |
= |
12
inches |
| 1
yard |
= |
3
feet = 36 inches |
| 1
mile |
= |
1760
yards = 5280 feet |
|
|
Units
of Time
|
| 1
minute |
= |
60
seconds |
| 1
hour |
= |
60
minutes |
| 1
day |
= |
24
hours |
|
| Units
of Weight
|
| 1
pound |
= |
16
ounces |
| 1
ton |
= |
2,000
pounds |
|
|
Units
of Volume
|
|
cup |
= |
8
fluid ounces |
| 1
pint |
= |
2
cups |
| 1
quart |
= |
2
pints |
| 1
gallon |
= |
4
quarts |
|
|
Changing Units Within the US/English
Units
To change a measurement from
one unit to the other, multiply by a unit ratio
that has both the original unit and the new unit.
For example:
166 cups = x pints
The ratio between cups and pints is 1 pint = 2
cups so we set up our ratio like this:
166 cups = 166 cups/ 1 x 1
pint / 2 cups
The "cups" cancel out and we are left
with:
166 cups = 166/2 pints
166 cups = 83 pints
There may be times when you have to do more than
one step to get to what you are looking for. For
example if we wanted to change 166 cups to gallons.
Notice how we will need to find pints then quarts
and then finally gallons which is what we are looking
for. For example:
First you need to change cups to pints.
166 cups = 166 cups / 1
x 1 pint/2 cups
166 cups = 83 pints
Now you need to change pints to quarts.
83 pints = 83 pints / 1
x 1 quart/2 pints
83 pints = 41.5 quarts
Lastly, you need to change quarts to gallons
to get your final answer.
41.5 quarts = 41.5 quarts
/ 1 x 1 gallon/4 quarts
41.5 quarts = 10.375 gallons
Therefore we found 166 cups to
equal 10.375 gallons. |
Adding Units of Measure
To add measurements in more than
one unit line up the units in columns and then add
column by column. Finish by simplifying your answer
by combining smaller units to make larger units whenever
possible. For example:
Add the following:
| |
2 hours 26 minutes
19 seconds |
| + |
5 hours 52 minutes 45 seconds |
 |
| |
7 hours 78 minutes 64
seconds |
To simplify your answer you remember that there
are 60 minutes in an hour and 60 seconds in a minute.
So you need to rewrite the following:
78 minutes = 1 hour 18 minutes
64 seconds = 1 minute 4 seconds
Now combine your answers to get the following:
7 hours + 1 hour + 18 minutes + 1 minute + 4
seconds
8 hours 19 minutes 4 seconds
|
Subtracting Units of Measure
To subtract measurements line
up the units in columns, replace larger units where
needed to make smaller units, and then subtract by
columns. For example:
Subtract the following:
5 hours 6 minutes 21 seconds
- 1 hour 45 minutes 55 seconds
You are unable to subtract 55 seconds from 21 seconds
so you need to go to the minutes column and take
1 of the 6 minutes and change it to 60 seconds and
add it to the 21 seconds already there. So you now
have this:
5 hours 5 minutes 76 seconds
- 1 hour 45 minutes 55 seconds
You can subtract the seconds column, but now you
go to the minutes column and you are unable to subtract
45 minutes from 5 minutes. Take 1 hour from the
5 hours there and change it to 60 minutes and add
it to the 5 minutes already there. So now we have
the following:
4 hours 65 minutes 76 seconds
- 1 hour 45 minutes 55 seconds
3 hours 20 minutes 21 seconds
You get a final answer of 3 hours
20 minutes 21 seconds. |
Fahrenheit and Celsius
Changing from Celsius to Fahrenheit
Use the following formula to change degrees Celsius
to degrees Fahrenheit where F equals degrees Fahrenheit
and C equals degrees Celsius:
F = 9C/5 + 32
Changing from Fahrenheit to Celsius
Use the following formula to change degrees Fahrenheit
to degrees Celsius where F equals degrees Fahrenheit
and C equals degrees Celsius:
C = 5(F-32)/9
|
Relationships Between US and Metric
Units
| Length
|
1
yard |
equals
approximately |
.915
meter |
| 1
foot |
equals
approximately |
.305
meter |
| 1
inch |
equals
approximately |
2.54
centimeters |
| 1
meter |
equals
approximately |
39.37
inches |
| 1
kilometer |
equals
approximately |
.625
miles |
| 1
mile |
equals
approximately |
1.6
kilometers |
| Volume |
1
liter |
equals
approximately |
1.057
quarts |
| Weight
|
1
pound |
equals
approximately |
454
grams |
| 1
kilogram |
equals
approximately |
2.2
pounds |
|
Perimeter
To find the perimeter of a polygon
or geometric figure, you find the distance around
it. You add the lengths of all sides to arrive at
the perimeter. When you find perimeter, you are working
with only one dimension as you measure around the
figure. Since you are only measuring and adding the
lengths around the figure, the units are labeled as
one dimension, usually just cm, ft, yd, mi, or others.
The units are NOT squared or cubed when finding
perimeter because you are working with one dimension. |
To find the area of a rectangle,
use the formula, L x W, where L is the length of the
rectangle and W is the width of the rectangle. When
finding the area of a rectangle, your results will
be in the units of measurement squared. The reason
the units are labeled squared is because you are working
with only two dimensions when working with area, length
and width. This is often represented as the
units of measure squared or to the second power. For
example, 15 cm2 or it may be written
as 15 squared cm. A = lw |
Area of a Triangle
To find the area of a triangle,
you use the formula, 1/2 x b x h, where b represents
the base of the triangle and where h represents the
height of the triangle. When finding the area of a
triangle, your results will be in the units of measurement
squared. The reason the units are labeled squared
is because you are working with only two dimensions
when working with area, length and width. A = 1/2
bh |
Volume of a Rectangle
One way to find the volume of
a rectangle is to multiply the dimensions, the length,
the width, and the height of the rectangle. Since
we find volume of a rectangle using three dimensions,
length, width, and height, the answer will be in units
cubed. This is often represented as the units of measure
cubed or to the third power. For example, 12 cm3 or
it may be written as 12 cubic cm. You use the following
formula: V = lwh |
Example
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