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Question: The ratio between pico and giga is (A) \({10^{21}}\) (B) \({10^{ - 21}}\) (C) \({10^{14}}\) ...

The ratio between pico and giga is
(A) 1021{10^{21}}
(B) 10−21{10^{ - 21}}
(C) 1014{10^{14}}
(D) 108{10^8}

Explanation

Solution

Hint
To solve this question, we can use any pico and giga on any unit and make its conversion. Then, we would get the required ratio. The metric prefixes are used to indicate the multiple of the unit with which it is being used. The unit prefix Giga equals the ten raised to the power nine of the unit.

Complete step by step answer
We know that one pico-metre contains 10−12{10^{ - 12}} metres.
That is, 1pm=10−12m1pm = {10^{ - 12}}m (i)
Also, we know that one giga-metre contains 109{10^9} metres.
That is, 1Gm=109m1Gm = {10^9}m (ii)
Dividing (i) by (ii), we get
⇒1pm1Gm=10−12109\Rightarrow \dfrac{{1pm}}{{1Gm}} = \dfrac{{{{10}^{ - 12}}}}{{{{10}^9}}}
⇒1pm1Gm=10−12×10−9\Rightarrow \dfrac{{1pm}}{{1Gm}} = {10^{ - 12}} \times {10^{ - 9}}
On solving, we get
⇒1pm1Gm=10−21\Rightarrow \dfrac{{1pm}}{{1Gm}} = {10^{ - 21}}
Or, picogiga=10−21\dfrac{{pico}}{{giga}} = {10^{ - 21}}
So, the ratio between pico and giga is 10−21{10^{ - 21}}
Hence, the correct answer is option (B), 10−21{10^{ - 21}}.

Additional Information
Along with giga and pico, there are some other important prefixes of units too in physics. They, along with their symbols and multiplication factors, are listed in the following table.
Different prefixes are used for units of quantities in different fields of physics.
Prefix
Symbol
Multiplication Factor
Atto
a
10−1810^{-18}
Femto
f
10−1510^{-15}
Nano
n
10−910^{-9}
Micro
μ\mu
10−610^{-6}
Milli
m
10−310^{-3}
Centi
c
10−210^{-2}
Deci
d
10−110^{-1}

Note
The metric prefixes are used to indicate the multiple of the unit with which it is being used. The unit prefix Giga equals the ten raised to the power nine of the unit. It is used for larger quantities or whole units. It is generally used as a unit of frequency. More famously, it is used as a unit prefix of memory with the base unit being byte. While the prefix Pico is used for measuring very small lengths. This unit is so small that its use is limited to the fields such as nuclear physics, quantum physics etc. It is generally used as a unit prefix for the wavelength of waves.