Question

What is the value of 1mg in kg ?
A) ${10^6}$
B) ${10^{ - 6}}$
C) ${10^{ - 3}}$
D) ${10^3}$

Answer 1

mg is short form of milligram and $1mg = {10^{ - 3}}gm$ also when we deals with the units in kg there we use the conversion factor as $1gm = {10^{ - 3}}kg$. Putting all these values and then simplifying we get the conversion of milligrams in kilograms.

Complete step by step answer:
We know that $1mg = {10^{ - 3}}gm$ & $1gm = {10^{ - 3}}kg$.
Rearranging the equation we get with
$\Rightarrow 1gm = {10^3}mg$
$\Rightarrow 1kg = 1000gm$
Converting it in scientific notation, we get.
$\Rightarrow 1kg = {10^3}gm$ putting the value, $1gm = {10^3}mg$
$\Rightarrow 1kg = {10^3} \times {10^3}mg$
Simplifying the equation we get with
$\Rightarrow 1kg = {10^6}mg$
$\Rightarrow 1mg = \dfrac{1}{{{{10}^6}}}kg$
Simplifying the equation we get with
$\Rightarrow 1mg = {10^{ - 6}}kg$.${10^1}$
Since $1mg = {10^{ - 6}}kg$.

Hence, option (B) is the correct answer.

Additional information:
Here this table is given to provide more information about the conversion of units.

SI PREFIX	SI SYMBOL	SI UNIT CONVERSION FACTOR	FACTOR (POWER)	FACTORLANGUAGE
Mega	M	1 megametre =100000 metres	${10^6}$	Million
Kilo	K	1 kilometre = 1000 metre	${10^3}$	Thousand
Hecto	h	1 hectometre = 100 metre	${10^2}$	Hundred
Deca	da	1 decametre = 10 metre		Ten
m	1 metre = 1 metre	${10^0}$	One
Deci	d	1 decimetre=0.1 metres	${10^{ - 1}}$	Tenth
Centi	c	1centimetre=0.01 metres	${10^{ - 2}}$	Hundredth
Mili	m	1milimetre=0.001 metres	${10^{ - 3}}$	Thousandth
Micro	$\mu$	1 micrometre=0. 000 001 metres	${10^{ - 6}}$	Millionth
Nano	n	1 nanometre=0. 000 000 001 metres	${10^{ - 9}}$	Billionth
Pico	p	1 picometre=0.000 000 000 001 metres	${10^{ - 12}}$	Trillionth
Femto	f	1 femtometre=0.000 000 000 000 001 metres	${10^{ - 15}}$	Quadrillionth
Atto	a	1 attometre=0.000 000 000 000 000 001 metres	${10^{ - 18}}$	Quintillionth
Zepto	z	1 zeptometre=0.000 000 000 000 000 000 001 metres	${10^{ - 21}}$	sextillionth
Yocto	y	1 yoctometre=0.000 000 000 000 000 000 000 001 metres	${10^{ - 24}}$	septillionth

Note:
In physics, mathematics and chemistry also where we have to deal with the bigger quantity and also the smaller quantity as we are confronting in daily use, a conversion factor is used to convert a measured quantity to a different unit of measure without changing the relative amount.
Units behave just like numbers in products and quotients, they can be multiplied and divided.