Question

What is the value of $ 5.84 \times {10^{ - 3}}mg $ in kilograms?
A. $ 5.84 \times {10^{ - 6}}kg $
B. $ 5.84 \times {10^3}kg $
C. $ 5.84 \times {10^{ - 1}}kg $
D. $ 5.84 \times {10^{ - 9}}kg $

Answer 1

Hint: In this question we have to convert mg into kg. Here mg stands for milligram. We will use the basic conversion formulas to solve this, such as $ 1mg = {10^{ - 3}}gm $ , but this value is in grams, we need to get kilograms. So we will apply another formula to convert milligram into kilogram i.e. $ 1mg = {10^{ - 6}}kg $. By putting these values and then simplifying we get the conversion of milligram in kilograms.

Complete step-by-step answer:
Here we have been given
 $ 5.84 \times {10^{ - 3}}mg $
We know that
 $ 1mg = {10^{ - 6}}kg $
So for $ 5.84 \times {10^{ - 3}}mg $ , we can multiply this value i.e.
 $ 5.84 \times {10^{ - 3}} \times {10^{ - 6}} $
We know the exponential formula which says that
 $ {a^m} \times {a^n} = {a^{m + n}} $
Here we have
  $ a = 10,m = - 3,n = - 6 $
So by applying the formula we can write
 $ 5.84 \times {10^{ - 3 + ( - 6)}} $
It gives us
 $ 5.84 \times {10^{ - 3 - 6}} = 5.84 \times {10^{ - 9}}kg $
So the required answer in kilogram is $ 5.84 \times {10^{ - 9}}kg $
Hence the correct option is (D) $ 5.84 \times {10^{ - 9}}kg $
So, the correct answer is “Option D”.

Note: We should know how to derive the formula. We know
  $ 1mg = {10^{ - 3}}gm $ And,
 $ 1gm = {10^{ - 3}}kg $
By rearranging the equation we can write
 $ 1kg = 1000gm $ .
We can write this also in exponential form i.e.
 $ 1kg = {10^3}gm $ .
By putting the value
  $ 1gm = {10^3}mg $
 $ 1kg = {10^3} \times {10^3}kg $
Simplifying the equation we get
  $ 1kg = {10^6}mg $
Or we can write it as
 $ 1mg = \dfrac{1}{{{{10}^6}}}kg $
We know the formula that $ \dfrac{1}{m} $ can also be written as
 $ \dfrac{1}{m} = {m^{ - 1}} $ .
So the above equation can also be written as
 $ 1mg = {10^{ - 6}}kg $ .