Question

How many micrograms are there in $2.45 \times {10^3}$ grams?

Answer 1

To answer this question we should know the conversion factor. To convert the gram to microgram we should know the relation between gram and microgram. There is a fixed relationship which we have to remember always. One microgram is the one millionth of the unit that we are considering. By using the conversion factor or relation between gram and microgram we will determine the answer.

Complete answer:
One millionth of a gram is known as a microgram or we can say one gram is equal to one million. So, $2.45 \times {10^3}$ grams will be equal to,
$1$ gram = ${10^6}$ microgram.
$2.45 \times {10^3}$gram = $2.45 \times {10^3}\, \times \,{10^6}$ microgram.
= $2.45 \times {10^9}$ microgram.
So, $2.45 \times {10^9}$micrograms are there in $2.45 \times {10^3}$ grams.

Therefore, $2.45 \times {10^9}$ micrograms is the correct answer.

Additional information: Here, we are converting the unit from gram to microgram so this is known as unit conversion. The factor which we use for the unit conversion is known as conversion factor such as here, the conversion factor is multiplication with${10^6}$.
When we convert a unit into another, we always multiply with the unit in which we want to convert and divide with the unit which we want to replace.
Here, we want to replace the gram from microgram. So, first we find the relation between gram and microgram which is $1$ gram = ${10^6}$ microgram. Then we multiply with ${10^6}$microgram because we want our answer in microgram and divide with $1$ gram because we want to remove the gram. Similarly by knowing the conversion factor we can convert any unit.

Note: The symbol used for the representation of the microgram is ${\text{\mu }}$g where, ${\text{\mu }}$ represents the micro and g represents the gram. We can also do the vice versa. If we have to calculate the gram from $2.45 \times {10^9}$ micrograms then,
We know, ${10^6}$ microgram = $1$ gram
So, $2.45 \times {10^9}$ microgram in gram =$\dfrac{{2.45 \times {{10}^9}}}{{{{10}^6}}}$