Question

Which of the following represents the smallest quantity?
A.$1230ng$
B.$1.230\times {{10}^{-4}}g$
C.$1.230\times {{10}^{-6}}kg$
D.$1.230\times {{10}^{4}}\mu g$

Answer 1

-The standard unit of weight is kilograms, denoted by $kg$ according to the international system of units, which is abbreviated as $SI$ unit.
-International system of units is a modernised form of the metric system which is the only official system of measurements generally, in all countries.

Complete step by step answer:
We know that the international system of units, which is denoted as $SI$ unit of mass of a substance is kilograms. If we consider the given question the quantities of the substance given in the options, are in terms of mass. But, all the options have different units, and so they are not comparable this way. In order to compare their quantities, only numbers are not enough, we need to look at the units too. For instance, you may have noticed that it is been told more than often to take care of the units, while doing calculations in physical chemistry or anything which involves units. There is a huge difference between $10km$ and $10m$, even though they have the same number $10$, they have different units $km$ and $m$, as $10km=1000m$. So, out of the two quantities, $10km$ was the highest.
So, now in order to compare all these quantities given in the option, we will convert all the units to gram according to the units which are already assigned to the quantities.
In the first part the unit is nano-grams, or $ng$, and we know that $1ng={{10}^{-9}}g$, so now we will convert $1230ng$ in terms of grams.
$1230\times 1{{0}^{-9}}g=1.230\times 1{{0}^{-6}}g$
As we can see that the quantity became much smaller after conversion.
Now for the next quantity, we can see that it is already present in terms of grams. So there is no need of conversion.
For the next quantity, it is present in terms of kilogram. And we know that $1kg=1000g$, so accordingly we will convert the whole quantity,
$1.230\times {{10}^{-6}}kg\times {{10}^{3}}=1.230\times {{10}^{-3}}g$
Now the next quantity is in micrograms so we will convert it to grams by using, $1\mu g={{10}^{-6}}g$, so the quantity would be,
$1.230\times {{10}^{4}}\mu g\times {{10}^{-6}}=1.230\times {{10}^{-2}}g$
Now if we consider the quantities in grams, and we can see that the quantity in option (a) is the smallest. Hence the correct answer is option A.

Note: In order to make two or more than two quantities comparable with each other, we should always convert all the quantities in the same unit. The $SI$ unit of mass is kilogram.
-Two quantities with different units are not comparable, so we cannot figure out the higher or the lower value of the quantity.