UNIT CONVERSIONS
UNIT CONVERSIONS
Why is it necessary to understand
how to convert between systems of
units?
UNIT CONVERSIONS
Why is it necessary to understand
how to convert between systems of
units?
Unfortunately many methods or units
were created for measuring the same
thing.
UNIT CONVERSIONS
Why is it necessary to understand
how to convert between systems of
units?
Unfortunately many methods or units
were created for measuring the same
thing. To understand the value of a
number it must be in a unit easily
understood.
UNIT CONVERSIONS
EXAMPLE: World currencies. Most countries have
their own unit of monetary value.
UNIT CONVERSIONS
The number on the bill might make you think a bill is
very valuable.
UNIT CONVERSIONS
But the real value becomes apparent when attempting to
purchase something.
UNIT CONVERSIONS
But the real value becomes apparent when attempting to
purchase something.
This boy has only a few
dollars worth of the
Zimbabwe Dollar (2008)
The Zimbabwe dollar
must not be worth much.
UNIT CONVERSIONS
In fact the Zimbabwe Dollar has become so low in value
that people have actually tossed them in the trash bin.
one $200 000 = $0.0002 US dollars!
UNIT CONVERSIONS
There have been many cases of drastic drops in value of
currency.
Here a street sweeper is
cleaning up discarded
money.
UNIT CONVERSIONS
The value in dollars is important because it is in a unit
you understand or are used to using.
UNIT CONVERSIONS
Of course the value of the dollar can fluctuate, which is
different from most things where conversions are
necessary.
UNIT CONVERSIONS
The equivalence or exchange rate is also known as the
CONVERSION FACTOR.
1
=
$3.67
( August 2011)
UNIT CONVERSIONS
Most conversion factors do not change. They are listed
in tables. It is important to be able to work from these
tables. These tables will always be provided.
Length
Volume
1 meter = 100 cm
1 meter = 1000mm
1 meter = 3.281 feet
1 inch = 2.54 centimeters
1 foot = 12 inches
1 foot = 0.308 meters
1 mile = 5280 feet
1 mile = 1.6 kilometers
1 liter = 1000 cm3
1 liter = .001 m3
1 liter = 0.0351 ft3
1 cm3 = 1cc
1 ft3 = 0.02832 m3
1 ft3 = 28.32 liters
1 ft3 = 7.477 gallons
Mass
1 slug = 14.6 kilograms
1 kilogram = 1000grams
Time
1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
1 year = 365 days (roughly)
UNIT CONVERSIONS
Unit conversions are based on the Identity Property of
Multiplication.
Simply Stated: The product of any number and 1 will be
the number you started with.
UNIT CONVERSIONS
Unit conversions are based on the Identity Property of
Multiplication.
Simply Stated: The product of any number and 1 will be
the number you started with.
Mathematically:
Z× 1 =Z
UNIT CONVERSIONS
Unit conversions are based on the Identity Property of
Multiplication.
Simply Stated: The product of any number and 1 will be
the number you started with.
Mathematically:
Z× 1 =Z
or
☺× 1 =☺
or
♣× 1 =♣
UNIT CONVERSIONS
So, as long as a number (X) is multiplied by 1 the
product will be the value (X).
UNIT CONVERSIONS
So, as long as a number (X) is multiplied by 1 the
product will be the value (X).
EXAMPLE:
4  48

 12
12   
4 4

UNIT CONVERSIONS
So, as long as a number (X) is multiplied by 1 the
product will be the value (X).
EXAMPLE:
4  48

 12
12   
4 4

Here the ratio has
the value of one.
UNIT CONVERSIONS
When units of measure are included a ratio may appear
that it is not equal to one but it is when the units are
taken into account.
EXAMPLE:
UNIT CONVERSIONS
When units of measure are included a ratio may appear
that it is not equal to one but it actually is when the units
are taken into account.
EXAMPLE: Because 12 inches equals 1 foot the
ratio:
12inches
1 foot
has a value of 1
UNIT CONVERSIONS
When units of measure are included a ratio may appear
that it is not equal to one but it actually is when the units
are taken into account.
EXAMPLE: Because 12 inches equals 1 foot the
ratio:
12inches
1 foot
has a value of 1
Numerator &
Denominator have
the same value
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
Start by writing the number given in the question over one
with the units.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet
1
Start by writing the number given in the question with the
units
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet
  __
1
Then multiply by a ratio and show where your solution
will be.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet
  __ inches
1
Write in the units you want to get to in the solution.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet inches

 __ inches
1
Write in the units you want to get to in the solution. These
units will also go in the numerator of your conversion
factor. This way the unit of inches comes out in the
solution.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet inches

 __ inches
1
feet
Now write in the unit you are converting from in the
denominator. This will make it cancel out when the values
are multiplied together.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet inches

 __ inches
1
feet
Notice the feet will cancel leaving only the unit of inches.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet inches

 __ inches
1
feet
Units cancel like numbers.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet 12inches

 __ inches
1
1 feet
Now put in the numbers for the conversion factor 1 foot =
12 inches.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet 12inches

 42inches
1
1 feet
To complete the work numbers in the numerator (top) are
multiplied and numbers in the denominator (bottom) are
divided.
Units are cancelled where they can be.
UNIT CONVERSIONS
Let’s see how a simple conversion factor is used.
EXAMPLE: How many inches are in 3.5 feet?
3.5 feet 12inches

 42inches
1
1 feet
Yes, this ends up simply being 3.5 x 12 but it is important
to understand how the units work on a simple problem so
that you can apply the same idea to more complicated
problems.
UNIT CONVERSIONS
Let’s try another simple example.
EXAMPLE: A sign states 150 kilometers to
Boston. How many miles is this?
150kilometers
  __ miles
1
Write the number with units over 1 multiplied by a ratio
equal to the units your trying to get to.
UNIT CONVERSIONS
Let’s try another simple example.
EXAMPLE: A sign states 150 kilometers to
Boston. How many miles is this?
150kilometers
miles

 __ miles
1
kilometers
Put the units you are attempting to get to in the numerator
of the ratio.
Also put the units you are trying to cancel in the
denominator.
UNIT CONVERSIONS
Let’s try another simple example.
EXAMPLE: A sign states 150 kilometers to
Boston. How many miles is this?
150kilometers
1miles

 __ miles
1
1.6kilometers
Put the appropriate numbers in the conversion factor ratio
UNIT CONVERSIONS
Let’s try another simple example.
EXAMPLE: A sign states 150 kilometers to
Boston. How many miles is this?
150kilometers
1miles

 __ miles
1
1.6kilometers
Put the appropriate numbers in the conversion factor ratio
UNIT CONVERSIONS
Let’s try another simple example.
EXAMPLE: A sign states 150 kilometers to
Boston. How many miles is this?
150kilometers
1miles

 __ miles
1
1.6kilometers
Cancel units where possible.
UNIT CONVERSIONS
Let’s try another simple example.
EXAMPLE: A sign states 150 kilometers to
Boston. How many miles is this?
150kilometers
1miles

 93.75miles
1
1.6kilometers
Now you have division 150 / 1.6 = 93.75
Remember, numbers in the top are multiplied and
numbers in the bottom are divided.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
Now
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
This conversion includes a unit in the numerator and
denominator. This will require more than a single
conversion factor.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft
sec
Write the number given in the question with the feet in the
numerator and the seconds in the denominator.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft
miles
   ___
sec
hour
Multiply by two ratios and make it equal to the desired units.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft miles
miles


 ___
sec
hours
hour
Put the desired units into the ratios.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft miles
sec
miles


 ___
sec
ft
hours
hour
Put the units you are converting from into the ratios.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft miles
sec
miles


 ___
sec
ft
hours
hour
Notice how the units will cancel.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft 1mile 3,600 sec
miles


 ___
sec 5,280 ft
1hour
hour
Now write in the numbers for the conversion factors.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft 1mile 3,600 sec
miles


 ___
sec 5,280 ft
1hour
hour
Now write in the numbers for the conversion factors.
UNIT CONVERSIONS
Let’s try a conversion where the unit is more complex.
EXAMPLE: A bullet travels at 800 feet/second,
how many miles/hour is this?
800 ft 1mile 3,600 sec
miles


 545
sec 5,280 ft
1hour
hour
Complete the math: 800 ÷ 5280 x 3600 = 545