# Metric System of Measurement

*(Correctly called "SI")*

The metric system is a **system of measuring**. It has three main units:

m | the meter for length | |

kg | the kilogram for mass | |

s | the second for time |

we can measure

*nearly everything*in the world!

## Examples:

### Meter

The length of this guitar is

about **1 meter**:

When unfolded this ruler

measures **2 meters**:

### Kilogram

This gold bar has a mass

of **1 kilogram**:

A dictionary also has a mass of

about **1 kilogram**:

### Second

**1 second**is about as long as it takes

to say

*"one thousand and one"*

## Larger or Smaller

But what if we want to talk about really big or really small things?

Answer: we can use Metric Number Prefixes

- like "kilo" (a thousand)
- and "milli" (one thousandth)
- and so on

### Examples:

something that is 1,000 meters is a "**kilo**meter"

a very short time of **one thousandth** of a second is a "**milli**second"

In fact the kilogram already uses this method, as it's a **thousand grams**, a **kilo**gram.

Here is a quick summary of the special prefixes:

## Common Big and Small Numbers

Name | The Number | Prefix | Symbol |

trillion | 1,000,000,000,000 | tera | T |

billion | 1,000,000,000 | giga | G |

million | 1,000,000 | mega | M |

thousand | 1,000 | kilo | k |

hundred | 100 | hecto | h |

ten | 10 | deka | da |

unit | 1 | ||

tenth | 0.1 | deci | d |

hundredth | 0.01 | centi | c |

thousandth | 0.001 | milli | m |

millionth | 0.000 001 | micro | µ |

billionth | 0.000 000 001 | nano | n |

trillionth | 0.000 000 000 001 | pico | p |

### Examples:

A thousand meters is a kilometer and abbreviated **km** (k for kilo, m for meter)

A million liters is a megaliter and abbreviated **ML**

A millionth of a second is a microsecond and abbreviated **µs** (µ is the greek symbol "mu")

These prefixes are used for computers too! A megabyte (MB) is a million bytes, a gigabyte (GB) is a billion bytes, etc.

**How to remember?**

For large values (each one a thousand times bigger) say:

"kilo mega giga tera"

And for small values (each one a thousand times smaller) say:

"milli micro nano pico"

Try saying them both a few times, they sort of rhyme and become easy to remember.## Making Other Units

We can also **combine** the meter, kilogram and second to make new Units of Measurement!

### Example: Speed

Speed is how **far** something moves over a period of **time**

So it can be measured in **meters** per **second**

It means: **How many meters does something travel in one second**

We can write it as meters/second, or more simply m/s

Here are a few common units that are based on the **meter**, **kilogram** and **second**:

## Area

### Square Meter

Area is length by length, so the basic unit of area is a square that is 1 meter on each side, in other words one square meter.

The Unit is meters × meters, which is written m^{2}

## Volume:

### Cubic Meter

Volume is length by length by length, so the basic unit of volume is a **cube that is 1 meter on each side**, in other words one cubic meter.

The Unit is meters × meters × meters, which is written m^{3}

### Liter

A cube that is 1 meter on each side is also **equal to 1,000 liters**.

1 m^{3} = 1,000 Liters

Liter is abbreviated **L** (some people use lowercase **l**, but that looks too much like **1**).

So a liter is actually **one-thousandth** of a cubic meter.

1 Liter = \frac{1}{1000} m^{3}

Another way of thinking about a liter is:

- A box that is 0.1 meters (10 cm) on each side,
- One square meter that is millimeter thick.

## Time

### Hour

An hour is 60 minutes, and a minute is 60 seconds, so an hour is:

- 60 × 60 = 3,600 seconds

### Day

A day is 24 hours so:

- 1 day = 24 × 60 × 60 = 86,400 second

## Speed

### Speed in meters per second (m/s)

This is a combination of two units (meters and seconds) to make a new one (m/s).

If something is moving at 1 m/s it moves **1 meter every second**.

### Speed in kilometers per hour (km/h)

A kilometer has 1000 meters, and an hour has 3600 seconds, so a kilometer per hour is:

- 1000 / 3600 = 1/3.6 = 0.277... m/s

How did I know to make it **1000/3600**, and not 3600/1000 (the other way around)? Read how to Safely Convert From One Unit to Another.

## Acceleration

Acceleration is how fast velocity changes.

When a runner accelerates from **5 m/s** (5 meter per second) to **6 m/s** (6 meters per second) *in just one second*, they accelerate by **1 meter per second per second**!

And yes, "per second" is used twice!

It can be thought of as (m/s)/s but is usually written m/s^{2}

## Force

Force is usually measured in the Unit of Newtons, an important measurement in Physics and Engineering.

A Newton is how much force it takes to make **1 kg** accelerate at **1 m/s ^{2}**.

1 **Newton** = 1 **kg m/s ^{2}** (one kilogram meter per second squared).

So force is actually based on the **meter**, **kilogram** and **second**.

So **force is a combination of the three basic units**.

## SI

The Metric System had its beginnings back in **1670** by a mathematician called Gabriel Mouton.

The modern version, (since 1960) is **correctly called** "International System of Units" or "SI" (from the French "* Système International*").

So we should really call it "**SI**", but mostly people just call it "Metric".

A few special units are also needed to complete the SI System:

- ampere for electric current,
- kelvin for temperature,
- mole for the amount of substance, and
- candela for luminous intensity

So the complete list is:

Quantity | Name | Symbol |
---|---|---|

Length | meter | m |

Mass | kilogram | kg |

Time | second | s |

Electric Current | ampere | A |

Temperature | kelvin | K |

Amount of substance | mole | mol |

Luminous intensity | candela | cd |

All other units (such as speed, force, power and many more) are "derived units" that are defined using these seven base units.