How do the prefixes micro, nano, and pico relate to each other?


Solution:  

The following are the values of the prefixes used in question.

1 micro (µ) = 10⁻⁶ 

1 nano (n) = 10⁻⁹ 

1 pico (p) = 10⁻¹² 


Relation between micro and nano:

We know that

1 micro (µ) = 10⁻⁶

In order to get the desire relation b/w micro (10⁻⁶) and nano (10⁻⁹), We will multiply the R.H.S. by 10⁻³ ï½˜ 10³

1 micro (µ) = 10⁻⁶ ï½˜ 10⁻³ ï½˜ 10³   [∴ 10⁻³ ï½˜ 10⁺³ = 1]

1 micro (µ) = 10⁻⁶⁻³ ï½˜ 10³

1 micro (µ) = 10⁻⁹ ï½˜ 10³

1 micro (µ) =  10³ï½˜ 10⁻⁹

1 micro (µ) =  10³ nano (n)       (∴ 10⁻⁹ = n)

or

1 micro (µ) =  1000 nano (n)  



Relation between micro and pico:

We have 

1 micro (µ) = 10⁻⁶ 

In order to get the desire relation b/w micro (10⁻⁶) and pico (10⁻¹²), We will multiply the R.H.S. by 10⁻⁶ ï½˜ 10⁶

1 micro (µ) = 10⁻⁶ ï½˜ 10⁻⁶ ï½˜ 10⁶  
(∴ 10⁻⁶ ï½˜ 10⁶ = 1)

1 micro (µ) = 10⁻⁶⁻⁶ ï½˜ 10⁶

1 micro (µ) = 10⁻¹² ï½˜ 10⁶

1 micro (µ) =  10⁶ｘ 10⁻¹²

1 micro (µ) =  10⁶ p     ∴[ 10⁻¹² = pico (p) ]

or

1 micro (µ) =  1000,000 p  



Relation between nano and pico:

We have

1 nano (n) = 10⁻⁹

In order to get the desire relation b/w nano (10⁻⁹) and pico (10⁻¹²), We will multiply the R.H.S. by 10⁻³ ï½˜ 10³

1 nano (n) = 10⁻⁹ ï½˜ 10⁻³ ï½˜ 10³  
(∴ 10⁻³ ï½˜ 10³ = 1)

1 nano (n) = 10⁻⁹⁻³ ï½˜ 10³

1 nano (n) = 10⁻¹²ï½˜ 10³

1 nano (n) =  10³ï½˜ 10⁻¹²

1 nano (n) =  10³ pico (p)      (∴ 10⁻¹² = p)

or

1 nano (n) =  1000 pico (p) 

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