Measurement is a number that explains the dimension or lot of something. You deserve to measure countless things choose length, area, capacity, weight, temperature and time. In the united States, two key systems the measurement space used: the metric system and the U.S. Customary measure system. This topic addresses the measure of size using the U.S. Customary measurement system.

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Suppose you want to purchase tubing for a project, and you view two indications in a hardware store: $1.88 for 2 feet that tubing and also $5.49 for 3 yards that tubing. If both species of tube will job-related equally well for her project, which is the far better price? You must know around two units the measurement, yards and feet, in bespeak to recognize the answer.


Units of Length


Length is the street from one finish of an object to the various other end, or indigenous one thing to another. For example, the length of a letter-sized piece of file is 11 inches. The device for measuring length in the United says is based upon the four customary units of length: inch, foot, yard, and also mile. Below are examples to present measurement in each of this units.


Unit

Description

Image

Inch/Inches

Some civilization donate your hair to be made right into wigs because that cancer patients who have lost hair as a an outcome of treatment. One firm requires hair donations to it is in at least 8 inches long.

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Frame size of a bike: the distance from the center of the crank come the height of the seat tube. Frame size is commonly measured in inches. This framework is 16 inches.

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Foot/Feet

Rugs are commonly sold in typical lengths. One common size is a rug the is 8 feet wide and 11 feet long. This is often described as an 8 by 11 rug.

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Yard/Yards

Soccer areas vary some in your size. One official field can be any kind of length in between 100 and 130 yards.

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Mile/Miles

A marathon is 26.2 miles long. One marathon course is displayed in the map come the right.

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You have the right to use any type of of these four U.S. Customary measurement units to describe the length of something, however it makes more sense to use details units for specific purposes. For example, it makes more sense to describe the size of a rug in feet rather than miles, and also to define a marathon in miles fairly than inches.

You might need to convert between units the measurement. Because that example, you might want to express your height using feet and inches (5 feet 4 inches) or using just inches (64 inches). You need to understand the unit equivalents in order to do these conversions between units.

The table listed below shows equivalents and also conversion factors for the 4 customary systems of measure up of length.


Unit Equivalents

Conversion determinants (longer to shorter units that measurement)

Conversion Factors

(shorter to much longer units of measurement)

1 foot = 12 inches

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1 garden = 3 feet

1 mile = 5,280 feet

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Note that each of these conversion components is a ratio of same values, so each conversion factor equals 1. Multiply a measurement by a conversion factor does not readjust the dimension of the measurement in ~ all since it is the very same as multiplying by 1; it just transforms the devices that you room using to measure.


Converting between Units the Length


You deserve to use the conversion factors to transform a measurement, such together feet, come another kind of measurement, such together inches.

Note the there room many an ext inches because that a measurement 보다 there room feet for the exact same measurement, as feet is a much longer unit that measurement. You could use the conversion factor

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.

If a length is measured in feet, and also you’d choose to transform the length to yards, you can think, “I am convert from a much shorter unit to a longer one, therefore the length in yards will certainly be much less than the size in feet.” You can use the conversion factor .

If a street is measured in miles, and you want to know how numerous feet that is, you can think, “I am convert from a much longer unit of measurement come a shorter one, for this reason the variety of feet would be higher than the number of miles.” You might use the conversion element

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.

You can use the label method> to transform a length from one unit of measure to an additional using the conversion factors. In the factor label method, you main point by unit fountain to transform a measurement native one unit come another. Examine the example below to see how the element label an approach can be supplied to convert  feet right into an equivalent number of inches.


Example

Problem

How countless inches room in

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 feet?

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Begin through reasoning about your answer. Since a foot is much longer than one inch, this means the answer would certainly be higher than .

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Find the conversion element that compares inches and feet, v “inches” in the numerator, and also multiply.

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Rewrite the mixed number as an improper portion before multiplying.

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You deserve to cancel comparable units as soon as they show up in the numerator and also the denominator. For this reason here, release the comparable units “feet” and also “foot.” This eliminates this unit indigenous the problem.

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*

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Rewrite as multiplication the numerators and denominators.

Multiply.

 

Divide.

Answer

There are 42 inch in  feet.


Notice the by using the variable label an approach you can cancel the units out of the problem, simply as if they were numbers. You can only publication if the unit being cancelled is in both the numerator and denominator the the fractions you space multiplying.

In the trouble above, you cancelled feet and also foot leave you through inches, which is what you to be trying to find.

What if you had actually used the dorn conversion factor?

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You could not publication the feet since the unit is no the same in both the numerator and also the denominator. So if you finish the computation, you would still have actually both feet and also inches in the answer and no conversion would take place.

Here is one more example the a length conversion using the aspect label method.


Example

Problem

How countless yards is 7 feet?

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Start through reasoning about the size of her answer. Because a yard is longer than a foot, there will certainly be under yards. So your answer will be less than 7.

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Find the conversion factor that compare feet and also yards, v yards in the numerator.

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Rewrite the whole number as a fraction in order come multiply.

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*

Cancel the similar units “feet” and “feet” leaving just yards.

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Multiply.

Divide, and write together a mixed number.

Answer

7 feet amounts to

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 yards.


Note the if the units carry out not publication to give you the answer you room trying come find, you might not have used the correct conversion factor.

How many feet space in  miles?

A) 10,560 feet

B) 30 feet

C) 2,112 feet

D) 13,200 feet


Show/Hide Answer

A) 10,560 feet

Incorrect. There space 5,280 feet in a mile, so multiply , no 2, by 5,280. The exactly answer is 13,200 feet.

B) 30 feet

Incorrect. A mile is much longer than 30 feet. There space 5,280 feet in a mile, so multiply 5,280 through , no  by 12, to find the variety of feet in  miles. The exactly answer is 13,200 feet.

C) 2,112 feet

Incorrect. Multiply, don’t divide, 5,280 by . The exactly answer is 13,200 feet.

D) 13,200 feet

Correct. There space 5,280 feet in a mile, so main point  by 5,280 to acquire 13,200 feet.

Applying Unit Conversions


There room times when you will should perform computations on dimensions that are given in various units. Because that example, think about the tubing difficulty given earlier. You should decide i beg your pardon of the two choices is a better price, and you have to compare prices offered in different unit measurements.

In order to compare, you require to transform the measurements into one single, common unit the measurement. To be sure you have actually made the computation accurately, think around whether the unit you room converting to is smaller sized or bigger than the number friend have. Its family member size will certainly tell you even if it is the number you are trying to uncover is higher or lesser than the provided number.


Example

Problem

An inner decorator demands border trim for a home she is wallpapering. She needs 15 feet that border trim for the living room, 30 feet that border trim because that the bedroom, and 26 feet of border trim because that the dining room. How countless yards of border trim walk she need?

15 feet

+ 30 feet + 26 feet = 71 feet

You need to find the full length the border trim the is needed for all three rooms in the house. Because the dimensions for every room are offered in feet, you can include the numbers.

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How many yards is 71 feet?

Reason about the dimension of your answer. Since a garden is longer than a foot, there will certainly be under yards. Suppose your answer to be less than 71.

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Use the conversion factor .

Since “feet” is in the numerator and also denominator, you can cancel this unit.

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Multiply.

Divide, and write as a mixed number.

Answer

The internal decorator needs

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 yards of border trim.


The next example uses the element label technique to settle a trouble that calls for converting from mile to feet.


Example

Problem

Two runners were comparing how much they had trained earlier that day. Jo said, “According to mine pedometer, ns ran 8.3 miles.” Alex said, “That’s a little more than what ns ran. Ns ran 8.1 miles.” exactly how many an ext feet did Jo operation than Alex?

8.3 miles – 8.1 mile = 0.2 mile

0.2 mile =

You need to find the difference between the distance Jo ran and also the distance Alex ran. Due to the fact that both distances are given in the very same unit, you can subtract and also keep the unit the same.

 = ___ feet

Since the trouble asks for the distinction in feet, you must transform from miles to feet. How countless feet is 0.2 mile? Reason around the dimension of her answer. Since a mile is much longer than a foot, the distance when expressed as feet will be a number better than 0.2.

 

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 = ___ feet

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= ___ feet

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= ___ feet

Use the conversion variable .

 

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= ___ feet

*
= ___ feet

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= 1,056 feet

Multiply.

Divide.

Answer

Jo ran 1,056 feet more than Alex.


Now let’s revisit the inquiry from earlier.


Example

Problem

You are walking through a hardware store and notification two sales ~ above tubing.

3 yards of pipe A costs $5.49.

Tubing B sells because that $1.88 for 2 feet.

Either tube is acceptable for her project. I m sorry tubing is less expensive?

Tubing A

3 yards = $5.49

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Find the unit price because that each tubing. This will make it simpler to compare.

Find the cost per yard of pipe A by splitting the price of 3 yards that the tubing by 3.

Tubing B

2 feet = $1.88

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Tubing B is marketed by the foot. Discover the expense per foot by dividing $1.88 through 2 feet.

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$2.82 per yard

To to compare the prices, you need to have the very same unit the measure.

Use the conversion aspect , cancel and also multiply.

Tubing A: $1.83 per yard

Tubing B: $2.82 per yard

Compare prices because that 1 yard of each tubing.

Answer

Tubing A is much less expensive 보다 Tubing B.


In the difficulty above, you could additionally have discovered the price per foot for each sort of tubing and compared the unit price of each per foot.

A fence company is measure a rectangle-shaped area in bespeak to download a fence roughly its perimeter. If the length of the rectangle-shaped area is 130 yards and the broad is 75 feet, what is the full length of the distance to be fenced?

A) 410 yards

B) 930 feet

C) 710 feet

D) 465 feet


Show/Hide Answer

A) 410 yards

Incorrect. The distance about the rectangle is 2 times the length plus two times the width, but you cannot do this computation unless the units are the same. Transform yards to feet and also then compute. The correct answer is 930 feet.

B) 930 feet

Correct. 130 yards is identical to 390 feet. To find the perimeter, add length + size + width + width: 390 feet + 390 feet + 75 feet + 75 feet = 930 feet.

C) 710 feet

Incorrect. Transform 130 yards come feet by multiplying by 3. Then, double to obtain the street of the two long sides that the rectangle in feet. Street for the broad is already given in feet, so multiply by 2 to get the length of both brief sides that the rectangle. The correct answer is 930 feet.

D) 465 feet

Incorrect. Fencing is necessary for 4 sides, not just two sides. The correct answer is 930 feet.

Summary


The four straightforward units the measurement that are offered in the U.S. Customary measurement device are: inch, foot, yard, and mile. Typically, civilization use yards, miles, and sometimes feet to explain long distances. Measurement in inch is common for shorter objects or lengths.

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You need to transform from one unit of measure to one more if you are solving difficulties that encompass measurements involving much more than one type of measurement. Every of the units deserve to be convert to among the other units utilizing the table of equivalents, the switch factors, and/or the variable label method shown in this topic.