Units part IΙ

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Metric Prefixes

SI units are part of the metric system. The metric system is convenient for scientific and engineering calculations because the units are categorized by factors of 10.

prefixes I

Prefixes are words or letters written in front that change the meaning .

We know that the mathematical notation of 10-x is equal to 1 / 10x .

For example :

10-1 = 1 / 10 ,

10-2 = 1 / 10= 1 / 100 ,

10-3 = 1 / 103 = 1 / 1000 , etc .

Prefixes III

With prefixes we can express small or big quantities .

Prefixes II

We can see the meaninig in the table above .

The following table gives metric prefixes and symbols used to denote various factors of 10 :

Prefix Symbol Value Example
tera T 1012 Tbytes
giga G 109 Gbytes
mega M 106 Mhz
kilo k 103 Km
hecto h 103 hectoliter
deka da 101 dekagram
deci d 10-1 dm
centi c 10-2 cm
milli m 10-3 mm
micro μ 10-6 μm
nano n 10-9 nm

We need to see some examples .

word example

Example 1

From city A to city B the distance is d = 80 km . The distance in meters is :

An easy example , 1 km = 103 m .

d = 80 km = 80·103 m = 8000 m .

The distance in megameters (Mm) is :

1 Mm = 106 m .

the first step is the same as before :

d = 80 km = 80·103 m .

We know that 10+x·10-x = 10+x-x = 100 = 1 ,

we select 10+3·10-3 = 10+3-3 = 100 = 1 ,

because we must create the factor 10+6 ,

d = 80·10+3 m = 80·10+3·(10+3·10-3) m  = 80·(10+3·10+3)·10-3 m = 80·(10+6)·10-3 m ⇒

we have alreade created 10+6 factor ,

d = 80·10+6·10-3 m = 80·10-3·10+6 m ⇒

1 Mm = 10+6 m ,

d = 80·10-3 Mm = 0,08 Mm .

The distance in gigameters (Gm) is :

1 Gm = 109 m .

the first step is the same as before :

d = 80 km = 80·103 m .

We know that 10+x·10-x = 10+x-x = 100 = 1 ,

we select 10+6·10-6 = 10+6-6 = 100 = 1 ,

because we must create the factor 10+9 ,

d = 80·10+3 m = 80·10+3·(10+6·10-6) m = 80·(10+3·10+6)·10-6 m = 80·(10+9)·10-6 m ⇒

we have alreade created 10+9 factor ,

d = 80·10+9·10-6 m = 80·10-6·10+9 m ⇒

1 Gm = 10+9 m ,

d = 80·10-6 Gm .

Let’s see another example .

Example 2

My pen is l = 12 cm long , the lengh in meters is :

We can see from the table , 1 cm = 10-2 m ,

l = 12 cm = 12·10-2 m .

And finally

12 cm =  12·(1 / 102) m = 12 / 100 m = 0,12 m .

The lengh in millimeters is :

1 mm = 10-3 m .

the first step is the same as before :

l = 12 cm = 12·10-2 m .

We know that 10-x·10+x = 10-x+x = 100 = 1 ,

we select 10-1·10+1 = 10-1+1 = 100 = 1 ,

because we must create the factor 10-3 ,

l = 12·10-2 m = 12·10-2·(10-1·10+1) m = 12·(10-2·10-1)·10+1 m = 12·(10-3)·10+1 m ⇒

we have alreade created 10-3 factor ,

l = 12·(10-3)·10+1 m = 12·10+1·(10-3) m = 120·10-3 m ⇒

1 mm = 10-3 m ,

l = 120 mm .

The lengh in micrometers is :

1 μm = 10-6 m ,

the first step is the same as before :

l = 12 cm = 12·10-2 m .

We know that 10-x·10+x = 10-x+x = 100 = 1 ,

we select 10-4·10+4 = 10-4+4 = 100 = 1 ,

because we must create the factor 10-6 ,

l = 12·10-2 m = 12·10-2·(10-4·10+4) m = 12·(10-2·10-4)·10+4 m = 12·(10-6)·10+4 m ⇒

we have alreade created 10-6 factor ,

l = 12·10-6·10+4 m = 12·10+4·10-6 m ⇒

1 μm = 10-6 m ,

l = 12·10+4 μm .

word practice

Now you must practice .

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