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
$$\Rightarrow 1kg={10}^{6}mg$$
$$\Rightarrow 1mg={\displaystyle \frac{1}{{10}^6}}kg$$
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.