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Introduction to Units
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Introduction

In this lesson, you will review the concept of units, specifically perimeter, area, and volume. Units can tell you what a number means (e.g., 55 kilometers).


This video illustrates the lesson material below. Watching the video is optional.


What is a Unit?

Units describe the quantity and value of a number. Units are very important. Without units, you cannot reference what the number represents in a given circumstance. For example, if you go into a store and there is a shirt that has a tag with the number 3. The number 3 has no units and therefore does not provide enough information for you to know the cost of the shirt. The shirt needs to have a unit with the number 3 so customers have enough information to purchase the item or not. Think about these other examples:

  • A recipe. With no units, how can you make the food?
  • Temperature. There is a big difference between 30 degrees Fahrenheit and 30 degrees Celsius

A shirt that has a tag with the number 3.

Figure 1

Different Types of Units

There are different kinds of units. Note the examples below.

  • Length: m (meter)
  • Mass: kg (kilogram)
  • Time: s (second)
  • Electric Current: A (ampere)
  • Temperature: K (kelvin)
  • Intensity of Light: cd (candela)
  • Amount of Substance: mol (mole)

The metric system uses meters, meters squared (\(m^2\)), and meters cubed (\(m^3\)), as well as millimeters, centimeters, kilometers, and many other units. The metric system also uses grams and kilograms for weight.

Metric Units:

  • Kilo- 1000 units
  • Hecto- 100 units
  • Deka- 10 units
  • Deci- 0.1 units
  • Centi- 0.01 units
  • Milli- 0.001 units

Metric Conversions:

  • To convert to a larger unit, move the decimal point to the left or divide.
  • To convert to a smaller unit, move the decimal point to the right or multiply.

The United States usually uses units like inches and feet for length, inches and feet squared for area, and inches and feet cubed for volume. There are also yards, miles, and other units to represent longer lengths. Ounces are also used in volumes and weights. Weights can be measured in pounds as well which is abbreviated as ‘lbs.'

U.S. Customary Units:

  • Length
    • 12 in = 1 ft
    • 3 ft = 1 yd
    • 5,280 ft = 1 mi
    • 1,760 yd = 1 mi
  • Weight
    • 16 oz = 1 lb
    • 2,000 lb = 1 ton
  • Capacity
    • 16 fl oz = 1 gal
    • 2 pt = 1 qt
    • 8 pt = 1 gal
    • 4 qt = 1 gal
  • Time
    • 60 sec = 1 min
    • 60 min = 1 hr
    • 24 hr = 1 day
    • 7 days = 1 wk
    • 52 wk = 1 yr
    • 12 mo = 1 yr
    • 365 days = 1 yr

Temperature has three common unit scales: Celsius, Fahrenheit, and Kelvin. Kelvin units are used often in science. Time also has its own sets of units: seconds, minutes, hours, days, years, and even centuries. A candela is a unit used to describe the luminosity of something, and an ampere is used to describe electric current.

These are just a few of the many units that are used in the world on a daily basis.


Things to Remember


  • Units tell you what the number means.
  • There are many different things in the world that you need to know the units for.

Real World Application

What is a unit you use frequently in your life? You might use it in your work, home, cooking, or measuring. Anything you measure requires a unit.

Practice Problems

1. Which of the following units are used to measure temperature? (
Solution
x
Solution: b.
)
a. Ounces (oz)
b. Degrees Celsius (°C)
c. Kilograms (kg)
d. Inches (in)
2. Which of the following units are used to measure length? (
Solution
x
Solution: a.
Details:
A unit to measure length is meters (m).

Length is measured with a ruler or tape measure or something else that measures distance. Examples of common units that measure length are millimeters, centimeters, meters, kilometers, inches, feet, yards, miles, etc.

In the past, it was common for different cultures to use different units to measure length. For example, in Algeria, they used to measure length using a termin and a pic while in ancient China they used to use the Shang and Zhou.

In this question, the only unit to measure length is the meter. Pounds measure weight, liters measure volume, and Fahrenheit measures temperature, so these can not be used to measure length.
)
a. Meters (m)
b. Pounds (lbs)
c. Liters (L)
d. Degrees Fahrenheit (°F)
3. Which of the following units are used to measure area? (
Solution
x
Solution: c.
Details:
Area is the measurement of a surface. It is the measurement of a flat piece of space. Area is like the size of a piece of land or the amount of floor space that could be covered by a rug.

It takes two directions of length to measure area: length and width, or width and height, or some other appropriate combination. When these two lengths are multiplied together the units become squared or raised to the 2nd power.

Thus the units for area usually have an exponent of 2. However, this is not always the case. There are some units for area that specifically refer to area and thus don’t need the exponent.

Examples of this are the acre and hectare. In this question, the exponent 2 on \({\text{ft}}^2\) gives away that it is a measurement of area. A liter is a measurement of volume, Celsius is a measurement of temperature, and miles measure length.
)
a. Liter (L)
b. Degrees Celsius (°C)
c. Square feet (\({\text{ft}}^2\))
d. Miles (mi)
4. Which of the following units are used to measure area? (
Solution
x
Solution: c.
)
a. Quart (qt)
b. Degrees Celsius (°C)
c. Square centimeters (\({\text{cm}}^2\))
d. Miles (mi)
5. Which of the following units are used to measure time? (
Video Solution
| Transcript)
a. Minutes (min)
b. Pounds (lbs)
c. Dollars ($)
d. Centimeters (cm)
6. Which of the following units are used to measure weight? (
Video Solution
| Transcript)
a. Seconds (sec)
b. Kelvin (K)
c. Feet (ft)
d. Pounds (lbs)

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