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# Measurements

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To measure is to compare the magnitude of a physical property of an object or a system against a pattern or standard that can tell us its value. Measurements in everyday life include:

• Measuring the wind and meteorological conditions to allow planes to fly.
• Measuring the energy demand of a region, allowing the electric grid to work without fail.
• Measuring the demand for products in a supermarket
• Measuring wave and wind conditions so surfers and sailors can go out safely.
• Measuring the energy consumption in your home so the energy company knows the amount you need to pay.
• Measuring a person’s temperature to check if they are healthy.

Figure 1. The physical property 'length' is measured and then translated into units using a standard.

## How do measurements relate to units and physical quantities?

Units tell us the value of the physical quantity we are measuring.

The activity of measuring is done to an object to learn its properties (or physical quantity) and then compared against an accepted norm to obtain a value (the unit). See the example below:

You want to know the weight of a parcel. The weight is the physical quantity of the parcel. You need to compare this against a unit of measurement to know its value. The unit varies depending on the unit system you are using.

### Measuring using different unit systems

There are several different unit systems. The most universally accepted unit system is the International System of Units (SI). Other unit systems are the United States Customary System and the Imperial system.

Measurements using different systems can deliver different values, as they measure the same physical quantities using different units. An example of this is the definition of temperature for the Imperial system, which uses Fahrenheit.

The freezing temperature of water is 273.15 Kelvin in the SI and 32 F in the Imperial system.

## Carrying out measurements

Generally speaking, there are two methods for measurements: one is by reference, while the other uses formal units.

### Measuring by reference

The principle is simple: you take an object, and you use that object as a reference to measure a quantity.

An everyday example is using a spoon to measure sugar for your coffee. However, you can see the problem with this – spoons come in different sizes, and you could also be adding more sugar depending on how much you fill the spoon.

### Taking measurements by using formal units

This method involves using a standard so you can reproduce the measurement every time you need it.

Let’s say that you need 10 grams of sugar. You will need a scale, but now you can measure exactly 10 grams of sugar every time. You can add and remove sugar to get the correct measurement and reproduce this whenever you want a coffee.

The ability to reproduce values using an instrument as a reference is why unit systems are important in measurement.

### Taking accurate measurements

Accuracy is important when taking measurements. To achieve it, you should follow these instructions:

1. Set your instruments to zero.
2. If you have instruments that use marks to read results, always read the value with your eyes directly over the values - not to one side. If you are not careful when reading the values, parallax errors might occur.Figure 2. When using instruments with marks, ensure your eyes are directly over the mark to avoid parallax errors. Source: Manuel R. Camacho, StudySmarter.
3. Repeat your measurements if necessary. Many errors come from measurements that contain minor errors. You can reduce some errors by measuring several times and then averaging the results.

When you measure the time it takes for a pendulum to make a complete oscillation, if you use a timer, the time measured will depend on your reaction time. In this case, several measurements are necessary so you can calculate a more precise average value.

## Representing measurements in real life

To graphically represent your measurements in real life, you can use a plot. Plots are drawings that use ‘x’ and ‘y’ variables to relate the change of one value to another. To put it simply, a plot is the graphical relationship of two or more variables. Usually, x is named as the independent variable, and y is the dependent variable.

See the example of a plot below, representing how a pendulum movement decays over time.

Figure 3. Simple plot showing the time it takes for a pendulum to swing. The time shortens with each measurement. Source: Manuel R. Camacho, StudySmarter.

The variable ‘x’ represents the measurement. The first point is the first measurement, where it takes 2 seconds for the pendulum to come and go. After the first measured value x1, you take a second measurement x2, then x3, x4 and so on.

The second point is the second measurement x2. The pendulum moves less until it slowly comes to a stop. The marks on the plot show the values decaying over time.

## Measurements - Key takeaways

• Measurements compare the magnitude or value of a physical quantity against a pattern or unit of measurement.
• Measurements are important, as they allow us to know the values of variables we use in everyday life.
• We can measure by reference or by using a formal unit system. Measurements using a unit system with standard values (such as the SI) allow the reproduction of the measured values.
• We need to be careful when measuring values so we don’t produce any errors.

Measurements are the values obtained after comparing a physical property to a pattern or standard that can tell us their value.

To measure something means to compare the magnitude or value of a physical quantity against a pattern or unit of measurement.

We can measure by reference, compare to other objects, or measure by using formal units.

Units are an agreed standard, a value used as a reference to measure. An example of such standards are the SI units kilogram, metre, second, candela, etc.

## Final Measurements Quiz

Question

What does ‘to measure’ mean?

To compare the magnitude of a value against a standard or pattern.

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Question

What do we measure in an object?

We measure a physical quantity or property.

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Question

We need units when doing measurements. True or false?

True.

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Question

What is the advantage of using units when measuring?

It allows us to reproduce measurements.

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How can we graphically represent measurements?

We can represent measurements using a plot.

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Question

When measuring with a scale, we need to set the scale to 0 every time. True or false?

True.

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Question

What is the name of the error when we are not careful reading a value using marks on the instrument?

Parallax error.

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Question

State the three steps for taking correct measurements.

Set instruments to zero, read all values carefully, and repeat the measurements.

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Question

What is a plot?

A plot is the graphical relationship of two or more variables.

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Question

What are the two ways you can measure things?

Using formal units or by reference.

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Question

Are measurements, units, and physical quantities related?

Yes, they are.

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Question

How are measurements, units, and physical quantities related?

You ‘measure’ a ‘physical quantity’ using ‘units’.

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Question

When you make a measurement, what are you doing?

Comparing a physical quantity to a standard or accepted pattern.

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Question

When you track the speed of a car, what property are you measuring, and which units do you use?

Speed, km/h or mph.

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Question

When you check the weather, what property are you measuring, and which units do you use?

Temperature, Fahrenheit or celsius.

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Question

Usually, in a plot, what is the name given to ‘y’?

The dependent variable.

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Question

Usually, in a plot, what is the name given to ‘x’?

The independent variable.

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