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Article: Size and Scale

Introduction:

It is useful to know the approximate size of things. Is something bigger than a bread box? Will it fit through a doorway? Is it as big as it is supposed to be? These are all questions that we may find ourselves asking on a regular basis.

In Egyptian times, the length of an object was measured in Cubits. One Cubit corresponded to the distance from one’s elbow to the tip of ones middle finger. The Cubit could be divided into smaller segments, related to the size of different parts of the hand. However, it is easy to imagine that these sizes vary greatly from person to person. A Cubit measured on a small child would be very different than one measured on an adult. Through the ages, measurement systems became more standardized. The two systems used today are the English and Metric System.

The Metric System

In everyday life the English system of measurement with units like feet, gallons, and pounds is primarily used in the United States. Scientists and the rest of the world use the metric system of measurement with base units such as the meter, liter, or gram. The base unit is then multiplied or divided by powers of ten to represent larger or smaller measurements. Prefixes are used to relate the relative size of the measurement with respect to the base unit. Since the base unit for length is the meter the table below shows all the different prefixes that could be used to express length.

|Prefix |Measurement |Scientific Notation |

|Kilo- |1000 m |1 x 103 m |

|Hecta- |100 m |1 x 102 m |

|Deka- |10 m |1 x 101 m |

|BASE |1 m |1 x100 m |

|Deci- |0.1m |1 x 10-1m |

|Centi- |0.01 m |1 x 10-2 m |

|Milli- |0.001m |1 x 10-3 m |

|Micro- |0.000001 m |1 x 10-6 m |

|Nano- |0.000000001 m |1 x 10-9 m |

|Pico- |0.000000000001 m |1 x 10-12 m |

|Femto- |0.000000000000001 m |1 x 10-15 m |

1000 meters would be written as 1 kilometer. Other base units can be used as well. For mass, the base unit is the gram, so 1/100th of a gram would be written as 1 milligram. Often it is hard to visualize what those number really mean – especially since base units in the metric systems are not something we may use in our everyday life.

How big is a Kilometer?

There are plenty of things around the world that are on the scale of a kilometer. The world’s longest suspension bridge, Akashi Kaikyo Bridge, is just under 2 kilometers (km) long, measuring 1,991 meters (m). It would take you approximately 23 minutes to walk across this bridge. The Sears Tower, the tallest building in North America, measures ~0.5 km (527m) to the top of the antennae.

How big is a meter?

A meter is a little bit bigger than a yard. A lot of things in our everyday lives are around the same size as a meter. An elementary school student is one meter tall. However, most professional basketball players are at least 2 meters tall. Shaquille O’Neill, at 7’1”, is 2.1 meters tall. In the photo below he seems to tower over former President Bush.

How big is a centimeter?

A centimeter (cm) is 1/100th of a meter – meaning that if you cut up a meter stick into 100 equal pieces, each piece would be one centimeter in size. Your pinky finger is about 1cm wide. A marble is about 1-2 cam wide. Same goes for the width of a sugar cube.

How big is a millimeter?

A millimeter (mm) is 1/1000th of a meter. A dime is approximately 1mm thick. Grains of sand range from 0.1mm to 2mm in size.

So far all the objects listed from Kilometer to millimeter are all things that can be seen with your eyes. Some are easier to see than others, but you typically don’t need a special tool to see any of these objects. When things get smaller than a millimeter, it gets hard to see them with just your eyes.

How big is a micrometer?

A micrometer, also called a micron, is one thousand times smaller than a millimeter. It is equal to 1/1,000,000th (or one millionth of a meter). Things on this scale usually can’t be seen with your eyes.

The diameter of a hair, which is about 40-50 microns wide, is very hard to see without the use of a magnifying glass. A magnifying glass will help you see a dust mite. Dust mites are usually around 400 microns long.

Things that are just a few microns in size can’t be seen without a magnifying glass. However, a light microscope, like the one you use in Biology class, can help you see things this small. Red blood cells are 6-10 microns in diameter. Many types of bacteria typically measure 5-20 microns.

How big is a nanometer?

A nanometer (nm) is 1,1000 times smaller than a micrometer. It is equal to 1/1,000,000,000th or one-billionth of a meter. When things are this small, you can’t see them with your eyes, or a light microscope. Objects this small require a special tool called a scanning probe microscope. A virus (30-50nm) and DNA (2.5nm) are examples of nanometer sized objects.

Atoms are smaller than a nanometer. One atom measures `0.1 – 0.3nm, depending on the element.

Here are some other everyday objects measured in nanometers:

• One inch equals 25.4 million nanometers

• A sheet of paper is about 100,000 nanometers in diameter

• A human hair measures roughly 50,000 – 100,000 nanometers in diameter

• Your fingernails grow one nanometer every second

Article Q’s: Size and Scale

(Student Sheet)

Questions:

1. What is a Cubit?

2. Describe the problems with the Cubit.

3. Name the two systems of measurement used today and what parts of the world use each system.

4. a. What are the three base units of the metric system?

b. What do each of the metric system’s base units measure? (**use your brain)

5. What number is the metric system based on?

6. Why are prefixes important?

7. List an example of each of the following:

a. Kilometer =

b. meter =

c. centimeter =

d. millimeter =

e. micrometer =

f. nanometer =

8. What instrument is used to look at objects the size of micrometers?

9. What instrument is used to look at objects the size of nanometers?

10. a. List an example of something in this room that is ~1 meter long.

b. List an example of something in this room that is ~1-5 millimeters wide.

Article Q’s: Size and Scale

(Student Sheet - KEY)

Questions:

1. What is a Cubit?

An Egyptian unit of measurement that equals the distance from the elbow to the tip of the middle finger.

2. Describe the problems with the Cubit.

Each persons Cubit was a different length, it was not standardized. A child’s Cubit would be different from an adult’s.

3. Name the two systems of measurement used today and what parts of the world use each system.

English – United Stated

Metric System – Scientists and the rest of the World

4. a. What are the three base units of the metric system?

Meter, Gram, Liter

b. What do each of the metric system’s base units measure? (**use your brain)

Meter = length, Gram = mass, Liter = volume

5. What number is the metric system based on?

10

6. Why are prefixes important?

They are used to relate the relative size of the measurement with respect to the base unit.

7. List an example of each of the following:

a. Kilometer = Akashi Kaikyo Bridge, Sears Tower

b. meter = elementary school student

c. centimeter = pinky finger width, sugar cube

d. millimeter = width of a dime, sand grain

e. micrometer = width of a human hair, dust mite, red blood cell, bacteria

f. nanometer = Virus, DNA

8. What instrument is used to look at objects the size of micrometers?

Magnifying glass

9. What instrument is used to look at objects the size of nanometers?

Light microscope

10. a. List an example of something in this room that is ~1 meter long.

Answers will vary (ex. poster on the wall)

b. List an example of something in this room that is ~1-5 millimeters wide.

Answer will vary (ex. letter on their paper)

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