Question

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

Answer 1

Hint: 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.