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# Unit of Measurement|Definition & Meaning

## Definition

A **unit of measurement** is a certain **magnitude** of an **amount** that has been defined and acknowledged by **law** or **convention** and is used as a **standard for measuring** other amounts of the same kind.

Any **quantity** that can be **measured** is called a **physical quantity.** To measure a physical quantity, two things are needed. The first one is the **unit of measurement** that sets a **reference amount** of that physical quantity. The second one is the **numerical magnitude** that defines how many multiples of a physical quantity are being measured with reference to the **unit** **of measurement.**

## Explanation of Unit of Measurement

The following** figure** describes this **concept** with the help of an **example** of the measurement of a **flour bag:**

**Figure 1: Flour Example of Unit of Measurement**

Suppose that you wanted to **measure** a **bigger bag** of **flour** that you have in your store. Now you also have a **1kg bag** of flour **available** with you in the same store. For the sake of **simplicity,** let us assume that the **1 kg bag** is your **reference** and you choose it as your **unit of measurement.**

Now to **measure** the **amount** of **flour** available with you, you simply **compare** the available **amount with** the **standard** that you have set (that is 1kg bag). As the **figure shows,** you find out that you have an **equivalent** to **nine** 1kg bags of flour bags.

In this **example,** the smaller** 1kg bag served as your unit of measurement** while the **number 9** represented the **magnitude** of the measurement.

The above unit that you defined **can’t be used universally** since the 1kg bag you used may **lose** its **weight** over time, and there is a chance that everybody may not be **comfortable** using your unit of measurement for theirs. This, indeed, has been the **main problem** with such units.

Over the rich **history** of **mankind, many units** have been **devised** for many physical quantities in different parts of the **world.** Naturally, these different units of measurement have caused **many problems** in terms of global trade and interoperability.

Therefore, the international community felt the need to develop a **standardized set of units** of measurement to be used **worldwide.**

The worldwide acceptable units of the measurement system, known as the **international system of units,** define some basic units of some basic quantities. In fact, there are only **seven** such **units.** These units are called **base units,** and the physical quantities that these units measure are called **base quantities.**

The units of all other physical quantities can be **derived from** these **seven base units.** These are called **derived units,** and the physical quantities that they measure are consequently called **derived physical quantities** in this context. The following **figure shows** these **seven base units.**

**Figure 2: The Seven Base Units of Measurement**

These units include **second,** **meter, kilogram, candela, ampere, kelvin,** and **mole.** They are used to measure **time, distance,** **mass, the intensity** of **light, electric current, temperature,** and **quantity** of **matter.**

Each of these base units is actually **standardized.** One **second,** for example, is defined as the time **equivalent** of **9,192,631,770 cycles** or wavelengths **emitted** by the **cesium-133** atom when one of its electrons jumps from one energy level to another level. This is why we often hear that the **cesium clock** is the **standard clock.**

Similarly, **one meter** is defined as the **distance** traveled by a **photon** of **light** in the **vacuum** during a time equal to **299,792,458th part of** the standard **second.** Again, we are being very specific here.

**Figure 3: Definitions of second, meter, and kilogram**

**One kilogram** is defined as the mass of a special piece of alloy made of **platinum-iridium** kept securely at the **international bureau** of **weights** and **measures.**

## Prefixes of Units of Measurement

Sometimes or for some measurements, the **standard units** defined by the international community are either **too large** or **too small** for the purpose of **measurement.** For example, what if you wanted to measure the **mass** of one of your **hair.**

Now **kilogram** is **not** a **suitable** unit since its mass is very small compared to the mass defined by a kilogram. Similarly, what if you wanted to **measure your age?** We all know that **seconds** is a **very small unit** for this purpose.

To resolve this issue, **prefixes** were **introduced.** These are the **multiples added** to the **units** to make them **larger** or **smaller** as per the **requirement** of the **application.** Let us consider the **example** of prefixes of meter for simplicity and **understanding.**

**Figure 4: Prefixes of Meter**

We have all heard about **millimeters, centimeters,** and** decimeters.** These are the prefixes that reduce the size of the **meter** by **1/1000, 1/100,** and **1/10** of the **original scale** for the purpose of measurement of **smaller distances.** It can also be noticed that:

**1 meter = 10 decimeter = 100 centimeter = 1000 millimeter**

Similarly, we have also often used or heard of **kilometers.** One kilometer is equal to **1000 meters,** and it is used to **measure larger distances.**

## Derived Units of Measurement

As we mentioned earlier, many units of different physical quantities can be **derived** based on the **standard base units** (seven) given above. Now let us see how we do this. Consider the **example** of **speed.** Now we know that speed is defined as the **distance covered in unit time.** Mathematically:

\[ \text{Speed} = \dfrac{ \text{Distance} }{ \text{Time} } \]

Now to **find** its **derived units,** we simply **plug** in the **units** of **distance** and **time** in the above formula like so:

\[ \text{Unit of Speed} = \dfrac{ 1 \text{ meter} }{ 1 \text{ second} } \]

This implies that:

**Unit of Speed = 1 meter / second**

Hence, the **unit of speed** **is** **1 meter per second,** written as **1 m/s**. You can see how simple it is to derive or define new units based on our **existing system.**

## Numerical Problems

**Part (a):** Convert **100 millimeters into centimeters.**

**Part (b):** Convert **1 kilometer into decimeters.**

**Part (c):** Derive the **unit** of a physical quantity **X = (mass)(length).**

### Solution to Part (a)

Since:

**1 meter = 1000 millimeter**

**1 meter = 100 centimeter**

**1000 millimeter = 100 centimeter**

Dividing both sides by 10:

**100 millimeter = 10 centimeter**

Which is the required solution.

### Solution to Part (b)

Since:

**1 kilometer = 1000 meter**

**1 meter = 10 decimeter**

So:

**1 kilometer = 1000 x 10 decimeter = 10000 decimeter**

Which is the required solution.

### Solution to Part (c)

From the definition of physical quantity:

**X = (mass)(length)**

Its unit can be derived by plugging in the standard units of mass and length:

**Unit of X = (unit of mass)(unit of length)**

**Unit of X = (1 kilogram)(1 meter)**

**Unit of X = 1 kilogram meter**

Which can be symbolized by** 1 kgm.**

*All images/mathematical drawings were created with GeoGebra.*