# 3.1.1: Introduction to Customary Units of Length

- Page ID
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)## Customary Units of Length

Megan is planning a birthday party for her friend. She wants to hang a large "Happy Birthday" banner on the wall but needs to make sure she gets the right size banner to fit the space she has. The wall she wants to hang the banner on needs to be measured correctly so she can determine the banner **length**. The only problem is, Megan doesn't know which unit she should use to measure. She has three options: **inches**, feet or miles.

In this concept, you will learn about **customary units of length** **measurement** and their appropriate uses.

**Units of Length**

**Measurement** is a concept that appears all the time in everyday life. To measure something is to determine a size, amount, or degree of an object using tools or comparison of objects.

**Length** is the measurement of the distance between two points, two things or two places. To measure length, a unit of measurement is used. There are two different systems for measuring: customary and metric. This concept is about Customary Units of measurement.

The most common customary units of measurement are the inch, the **foot**, the **yard** and the **mile**.These units can be converted between one another; for example, there are 12 inches in 1 foot, 3 feet in 1 yard, 5,280 feet in 1 mile etc. An important skill in measuring is to know when to use each of these units of measurement so less conversions need to occur.

One **inch** is roughly the length of your thumb from the tip to the knuckle. The abbreviation for the inch is in.(for example, 5 in.) The ruler below shows what inches look like when marked on a ruler.

Small things are measured in inches. Here is a picture of a crayon. The length of the crayon can be determined in inches using this ruler.

The inch can also be divided into smaller segments or smaller units. This helps when objects do not measure to a perfect whole inch (which happens more often than not). On a ruler you can see the smaller inch segments of 14″,12″,34″.

The next largest customary unit is the **foot**. The abbreviation for measuring a foot is ft (for example, 3 ft). One foot is roughly the length from your elbow to the end of your fingers. A ruler is used to measure feet because a ruler is exactly one foot long.

On a ruler, there are 12 inches marked, which makes one whole foot. Larger objects are measured using feet instead of inches because it is a larger unit of measurement. Feet are commonly used in measurement for objects such as the length of a car, height of a door, or the distance between two objects.

Another customary unit of measurement is **yards.** The abbreviation for yards is yd (for example, 7 yd). There are three feet in one yard. Yards can be used to measure larger objects than would be measured with inches or feet.

It makes sense to use inches, feet and yards when measuring short distances or the length of objects or people. We use these customary units of measurement all the time in our everyday life.

To measure longer distances, the customary unit of **miles** is used. A mile is the longest customary unit of measurement. There are 5,280 feet in one mile.

**Examples**

Example 3.1.1.1

Earlier, you were given a problem about Megan and her banner decoration for her friend's birthday party.

Megan needs to use the appropriate unit of measurement to figure out the right length banner to hang on the wall. She needs to measure the wall length to determine the correct banner length. Her choices for measuring are inches, feet or miles.

**Solution**

First, Megan needs to think about the object she is measuring or actually stand in front of the wall she is planning to hang the banner on.

Next, Megan needs to consider the choices she has for measuring and rule out any units that do not make sense for this object. Miles are used to measure very far distances, not banners, so she can rule that choice out.

Then, Megan will match up the appropriate unit with the wall. Both inches and feet could be used, but inches are so small that it would take much longer to measure the wall than it should. Feet are the appropriate unit to measure a wall.

The answer is feet.

Megan will measure the wall in feet to determine the correct length of banner to fit that wall.

Example 3.1.1.2

Determine which unit of measurement to use to measure the length of a pencil.

**Solution**

First, try to find a real-life example of the object. If you do not have one, try to picture in your head what that object looks like.

Next, think about the customary units of measurement and how small or big they are. Our choices are inches, feet, yards or miles (in order from smallest to biggest).

Then, try to match an appropriate unit with the size of the object you are measuring. In this question, a pencil is rather small and does not even span the entire length of a ruler, which is 1 foot. The next smallest unit should be used then, which is the inch.

The answer is inches.

Example 3.1.1.3

What unit of measurement would be used to measure the height of a door?

**Solution**

First, find the object to be measured or picture it in your mind.

Next, think about your unit of measurement options and rule out ones that don't make sense. Miles would definitely not be needed to measure a door height, so we are left with inches, feet or yards.

Then, determine which unit is most appropriate. Yards are the largest and would require us to measure in much smaller segments than a whole yard. Inches are the smallest and would take a really long time to measure the height. Feet are just the right unit of measurement to use.

The answer is feet.

Example 3.1.1.4

What unit of measurement would be used to measure your sneaker?

**Solution**

First, find the object or think about what the object looks like.

Next, think about your measuring options. Miles and yards are both much longer than a sneaker those are ruled out.

Then, match the appropriate unit with the object. Some feet are longer than the length of a ruler (which is one foot, or 12 inches), but most feet are less than 12 inches, so a ruler would also be too large. Inches would be our only reasonable choice.

The answer is inches.

Example 3.1.1.5

What unit of measurement would be used to measure the distance between two cities?

**Solution**

First, think about the items to be measured (Cities are places, not objects, so picture how far apart they would be in your mind).

Next, think about your unit of measurement choices. None are ruled out since the length being measured is so large, but there are more appropriate choices than others.

Then, match the appropriate unit of measurement with the items to be measured. Long distances are never measured in inches or even feet. Yards can sometimes be used to measure distances, but usually distance between objects closer together like houses or sidewalks. Miles is the only reasonable choice to measure such a long distance between two locations.

The answer is miles.

### Review

Write the appropriate customary unit of measurement for each item.

- The height of a sunflower
- The depth to plant a seed in the soil
- The height of a tree
- The area of a garden plot
- The distance from a garden to the local farm store
- The length of a carrot
- A stretch of fencing
- The length of a hoe
- The distance between two seedlings planted in the ground
- The height of a corn stalk
- A piece of pipe for a water line
- The depth of a pool
- The distance across a lake
- The distance from your home to school
- The size of a paperclip
- The measure of a length of thread

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.1.

### Vocabulary

Term | Definition |
---|---|

Customary System |
The customary system is the measurement system commonly used in the United States, including: feet, inches, pounds, cups, gallons, etc. |

Customary units of length |
Customary units of length include: inches, feet, yards and miles. |

Foot |
A foot is a customary unit of measurement. There are 12 inches in 1 foot. |

Inches |
An inch is a customary unit of measurement, measured best by a ruler. |

Length |
Length is a measurement of how long something is. Examples of customary units of length are inches, feet, yards and miles. |

Measurement |
A measurement is the weight, height, length or size of something. |

Mile |
A mile is a customary unit for measuring distance. There are 5280 feet in 1 mile. |

Yard |
A yard is a customary unit of measurement. There are 3 feet in 1 yard. |

#### Additional Resources

PLIX Interactive: **Customary Units of Length: Giraffe Measurement**

Practice: **Introduction to Customary Units of Length**