Question

How many picograms are in $4.48 \times {10^{ - 11}}$ grams?

Answer 1

Hint: Here, we will use the concept of conversion of units. Both gram and kilogram are measuring units of weight and gram is a larger unit than a picogram. We will multiply the conversion faction to the given dimension to get the required answer.

Complete step-by-step solution:
We know that one picogram is equal to ${10^{ - 12}}$ grams. We can also say that in ${10^{ - 12}}$ grams, there is one picogram.
By the unitary method, this implies that one gram is equal to $\dfrac{1}{{{{10}^{ - 12}}}}$ picograms, or equal to ${10^{12}}$ picograms.
Now, according to the above question we have to find out the number of picograms in $4.48 \times {10^{ - 11}}$ grams. Since we found above that one gram is equal to ${10^{12}}$ grams, the number of picograms in the given number, $4.48 \times {10^{ - 11}}$ of grams will be given by
$n = 4.48 \times {10^{ - 11}} \times {10^{12}}$
Using the properties of the exponents, we have ${a^m}{a^n} = {a^{m + n}}$. Therefore, the above expression is written as
$n = 4.48 \times {10^{ - 11 + 12}}$
$ \Rightarrow n = 4.48 \times {10^1} = 44.8$

Hence, there are $44.8$ picograms in $4.48 \times {10^{ - 11}}$ grams.

Note:
To convert a dimension given in one unit into another unit we have to use a converting factor. Generally, for converting some dimensions into smaller units of measurement then we will multiply it with the converting factor. However, for converting some dimensions into a larger unit of measurement then we will divide it by the converting factor. Some of the other weight measuring units are pounds, kilograms etc. A pound is generally not used as an Indian weighing system, a kilogram is the weighing unit which is generally used in the Indian weighing system. A pound is generally the weighing unit used in the foreign weighing system.