**Measurement**

What are measurements?

A measurement is a determination of

the amount of something.

Example: 1 Gallon of milk is a measurement of the amount of milk a person may have.

All measurements must have a unit and a value for it to be meaningful

6 lb burrito

6 is the number value and lbs. (pounds) is the unit.

A unit is a standard amount that everyone agrees on.

English System vs International System

English System

This system is used for everyday measurements in the United States.

Only one or two countries outside the US use the system.

The English system units include some of the following:

Miles, Feet, Inches, Pounds, Pints, Quarts, Gallons, Cups, and Teaspoons.

International System (SI)

This system was developed in France in the 1800's.

It was quickly adopted by most European and South American countries.

The goal of this system was for all units of measurement to be related and for the units to form a base-10 system.

Almost all fields of science use SI units because they are so much easier to work with due to the base-10 system.

This system includes units like kilometers, meters, milliliters, grams, micrograms, watts, joules, and many others.

Why is the SI system preferred?

In the English system, there are 12 inches in 1 foot, 3 feet in a yard, and 5,280 feet in 1 mile.

These numbers are not easy to remember!

In the International system, there are 10 millimeters in 1 centimeter, 100 centimeters in 1 meter, and 1,000 meters in 1 kilometer.

Factors of 10 are simply easier to remember and work with.

It's all about the prefix

The metric system makes use of prefixes to change the size of a unit. For example, I can add the prefix "kilo" to the unit gram to get the unit "kilogram" which is equal to 1,000 grams.

Measurements should be made and recorded using appropriate units and prefixes. For example, I would use centimeters to measure the length of my pencil but would use kilometers to measure the distance to Murfreesboro.

SI Prefixes

The use of prefixes before the SI units makes life much easier.

The unit prefix determines the factor of ten to be used in the number value.

For example the prefix "giga" means a factor of 10. This means that 1 gigabyte is equal to 1,000,000,000 bytes. So 1 gigabyte is 1 billion times larger than 1 byte!

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What are you measuring?

Is it something that is very small or extremely large?

Is it a measurement of length/distance, mass, volume, or time?

Unit first, prefix second

The type of measurement being made will determine the unit to be used.

For example, mass is measured in base units called grams (g), time in seconds (s), distance/length in meters (m).

After the unit has been decided, a prefix may be necessary. If the thing being measured is considerably larger or smaller than the base unit, then you probably need a prefix.

Let's do a measurement together

Suppose I am asked to measure the length of common field mouse. How am I going to do this?

I have been asked to measure the length of an object. The base unit for length is the meter. This is the first step of the measurement process - deciding what unit to use.

Next, I need to compare this base unit to the object I am measuring. The meter is considerably longer than a field mouse. I will need a prefix to have a better measurement.

Length of a mouse

As you can see, the mouse is quite small so the meter will be too large a unit to use for measuring its length. If I move down 2 powers of ten, I arrive at the prefix "centi" which is a factor of 10 . This means there are 100 centimeters in 1 meter. The average field mouse has a length of 15.2 cm or 152 mm (millimeters = 10 )

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Factors of Ten

One of the greatest and most convenient qualities of the International System is its use of prefixes which indicate a different factor of ten for the base unit. Simply changing the measurement by a single factor of ten can have a huge impact on the size of the measurement as this classic video can show.

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Scientific Notation

Sometimes, it is more convenient to list a number in scientific notation rather than change the prefix.

For example, our measurement showed that the avg. mouse is 152 mm long. This measurement, given in units of meters would be 0.152 meters.

Lets use scientific notation to write these two numbers differently even though they are the same length.

0.152 meters is 1.52 x 10 meters. 152mm would be written as 1.52 x 10 millimeters.

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Time

Time is used in two ways: a particular moment in time and a quantity of time.

The scheduled time for this class to end is 11:00am. This is an example of a particular moment in time. These moments can be past, present, or future.

This class is scheduled to last 1 hour and 25 minutes. This is an example of a quantity of time.

Time

Many problems in science use the unit "second" (s) when measuring time. However, you may need to use larger units such as minutes, hours, days, and even years.

Distance

Distance is the amount of space between 2 points or how far apart two objects are.

Distance is measured using units of length. The base SI unit for length is the meter (m).

The use of the metric prefixes allows us to measure great distances with appropriate units. For example the distance to the classroom door would be measured using meters, but the distance to Nashville would be measured in kilometers (adding the prefix kilo to the unit meter).

Using a meter stick

A meter stick is 1 meter long and is divided into 1,000 millimeters and 100 centimeters. This means there are 10 millimeters in each centimeter.

Converting Units

Is a kilometer a greater distance than a mile? If I can bench press 20,000 grams.... does this mean I'm.....Superman?!?

Unfortunately, the answer to both questions is NO!

We can use dimensional analysis to convert English and SI measurements from one to another.

Dimensional analysis is a method of using conversion factors and unit canceling to solve a unit conversion.

Conversion Factors

A conversion factor is a ratio that has a value of one and is used when setting up a unit conversion problem.

It is these factors that allow us to change measurements from English units to SI units and vice-versa.

Here are a few common conversion factors we will use in this class:

1 mile = 1.609 kilometers 1 inch = 2.54 centimeters

1 kilogram = 2.2 pounds 1 hour = 60 minutes

Unit Canceling

What if I want to know how fast I am driving is SI units like kilometers per hour? In this class, we will need to be able to convert the units from one system to another by canceling units we do not want.

(60 miles)/(1 hour) × (1.609 kilometers)/(1 mile) =96.54 kilometers per hour

Accuracy & Precision

Accuracy is how close a measurement is to the true value. Examples of accuracy are throwing a bull's eye in darts, making a basket in a basketball game, or a watch that gives a time that is very close to the official time.

Precision describes how close together repeated measurements or events are to one another. An example of precision would be hitting a target in the same area 5 consecutive times while shooting archery.

Resolution

Resolution refers to the smallest interval that can be measured. What is the resolution of the clock on the wall in this classroom? What about the scale below?

Comparing Measurements

Precise measurements must be reproducible by you and others. This means the same measurement can be made again in the exact same way.

In science, having the "same" measurements means they are not significantly different. Significant differences are differences that are much greater than the estimated uncertainty.

Significant differences

Not Significantly Different

If you expect a pay check for $1000 and you actually get $1002.

One gas station charging $3.09/gal and another $3.10/gal.

Significant Differences

How many seconds are listed on this stopwatch?

Estimated Error

When we estimate error or uncertainty in a data set, we will

assume

the average is the exact value. Our estimated uncertainty will be the average of the differences (use absolute values) between each measured value and the group average value.