UNITS OF
CONVERSION
Related topics: 1, 5.
Linear
Measure
Example 1. Convert 4.6 miles to feet.
Solution.
* Write 4.6 miles as a
fraction by dividing it by 1:
* Multiply this
fraction by 1, which we know is
equivalent to
because the numerator and the denominator measure the
same
length.
* Now the initial expression can be
written as
* Write the above fraction as two
fractions:
* Simplify to:
Example 2: Convert 4.6 kilometers to miles.
Solution:
* The Webster Dictionary
states that there are approximately
0.621 miles in 1 kilometer; therefore
4.6 kiometers are equivalent
to the fraction
* Simplify kilometers with kilometers, and then get
2.8566
miles
Square Measure
Example 3: Convert 180 square inches to square feet.
Solution:
* 180 square inches can be
written as 180 x 1 square inch.
* Since 1 square
inch can be written as 1 inch x 1 inch,
* 180
square inches can be written 180 x 1 inch x 1 inch.
* Note that 1 inch can be written as 1 inch x 1 and the
1 can be
written as a fraction where the numerator and the denominator
are
equivalent.
* Write 1 inch x 1
as
* 180 square inches = 180 x 1 inch x 1 inch =
180 x 1
inch x 1 x 1 inch x 1
which
means
* Multiply the fractions and rearrange
the numerator
and the denominator.
* Rewrite as five
fractions where as many fractions as
possible have an equivalent value of
1.
1.25 x 1 x 1 x 1 foot x 1
foot
* Note: 1 foot x 1 foot is the same as one square
foot.
* The answer is 1.25
square feet.
Cubic (Volume)
Measure
Example 4:What exactly does 1 cubic foot mean?
Answer: One cubic foot means 1 foot x 1 foot x 1 foot.
Solution: From the above table you can see a link between cubic feet and cubic yards.
* 50 cubic yards can
be written as 50 x 1 cubic yard.
* Since 27 cubic
feet is equivalent to 1 cubic yard,
the fraction
is equivalent to 1.
* Multiply 50 x 1
cubic yard by 1 in the equivalent form
from above to obtain the expression
as
* Multiply the two fractions, rearrange the
numerator
and write the fraction as a product of fractions so that some of
the fractions
have a value of 1:
* The answer is
1,350 cubic feet.
Problems
1. Convert 25,000 feet to miles.
2. Convert 10 decimeters to yards.
3. Convert 1400 yards to furlongs.
4. You have decided to carpet a 21-foot by 33-foot room in your house, and you have decided on a carpet that costs $22.00 per square yard. How much will it cost you to carpet the room?
5. Convert 6,000 square decameters to sections.
6. Convert 7 acres to square meters.
7. Convert 5,000,000 square feet to sections.
8. Convert 8 square yards to square centimeters.
9. Convert 86 square decimeters to square hectometers.
10. Convert 31.5 cubic centimters to cubic feet.
11. Convert 25,000 cubic feet to cubic yards.
12. Convert 10 cubic decimeters to cubic yards.
13. Convert 1400 cubic yards to cubic meters.