Pace Work. 10-D. Maths. 29.03.2021

Topic:Metric System of Measurement

1. Study the theory block:

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

With those three simple measurements
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 "kilometer"

a very short time of one thousandth of a second is a "millisecond"

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

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 m²

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 m³

Liter

A cube that is 1 meter on each side is also equal to 1.000 liters.

1 m³ = 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 = 11000 m³

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)? 

2. Do the task following the link