Question

What does a measurement of $3853$ $pg/mg$ means?

Answer 1

Every substance in nature possesses some physical and chemical properties which are measured by a number of ways which are commonly known as fundamental units. Fundamental units are considered as an independent unit which are not derived from other units.

Complete answer:
The SI units are used nowadays which are accepted worldwide and it includes total $7$fundamental quantities to describe the physical parameters of matter.
According to the SI unit system, mass or weight of any substance is expressed in terms of kilograms $Kg$.
We can convert kilograms into smaller units namely- grams, milligrams $\left( {mg} \right)$, nanograms $\left( {ng} \right)$, picograms $\left( {pg} \right)$, decigrams $\left( d \right)$any many other.
We can convert all these units in terms of grams as:

UNIT	SYMBOL	POWER (in terms of grams)
Gigagrams	$G$	${10^9}$
Megagrams	$M$	${10^6}$
Kilograms	$Kg$	${10^3}$
Grams	$g$	${10^0}$
Decigrams	$d$	${10^{ - 1}}$
centigrams	$cg$	${10^{ - 2}}$
Milligrams	$mg$	${10^{ - 3}}$
Micrograms	$\mu g$	${10^{ - 6}}$
picograms	$pg$	${10^{ - 12}}$

Unit $3853$ $pg/mg$ shows that one milligrams of substance contains $3853$ picograms of the sample.
From the table we already see that $1mg =$ ${10^{ - 3}}$ $g$
And $1pg$ $=$ ${10^{ - 12}}$ $g$
Hence, we can convert the mass of the compound in terms of grams as:
$3853$ $pg$ of sample contains $=$ $1$ $mg$ of compound
$1$ $pg$ of sample contains $=$ $\dfrac{1}{{3853}}$ $mg$ of compound
On deriving the mass in terms of grams we get-
$\dfrac{{1 \times {{10}^{ - 3}}}}{{3853 \times {{10}^{ - 12}}}}$ $g$
On solving the above equation, we get
$0.000259 \times {10^{ - 3 + 12}}$ $g$
On calculating the above equation, we get
$0.000259 \times {10^{ + 9}}$ $g$
This equation is written as:
$2.59 \times {10^5}$ $g$
This calculation has the significance that it shows that the sample is present $2.59 \times {10^5}$ times of the main compound.

Note:
SI units for other physical quantities are- litres for volume, second for time, kelvin for the temperature, ampere for current, candela for intensity of light, and mole for amount of any substance. Selection of units of measurement is helpful in calibrating all the other measuring devices.