Question

Find the value of : $1\% $ of $1\% $ of $25\% $ of $1000$ is:
A.$0.025$
B.$0.0025$
C.$0.25$
D.$0.000025$

Answer 1

Hint: This question can be easily solved just by multiplying the given numbers and converting the $\% $ sign as $\dfrac{1}{{100}}$. Also, in the end, converting the fraction into its decimal form would give us the required answer.

Complete step-by-step answer:
In this question, we have to find the value of:
$1\% $ of $1\% $ of $25\% $ of $1000$
Now, as we know, here ‘of’ stands for ‘multiplication’.
Also, $25\% $ can be written as $\dfrac{{25}}{{100}}$
Hence, rewriting the given question, we get,
$1\% $ of $1\% $ of $\dfrac{{25}}{{100}} \times 1000$
Now, the two zeros will cancel out from the numerator as well as the denominator.
$ = 1\% $ of $1\% $ of $250$
Again, $1\% $ can be written as $\dfrac{1}{{100}}$
Therefore, we get,
$ = 1\% $ of $\dfrac{1}{{100}} \times 250$
Now, cancelling out a zero from numerator as well as denominator, we get,
$ = 1\% $ of $\dfrac{{25}}{{10}}$
Again, writing $1\% $ as $\dfrac{1}{{100}}$, we get
$ = \dfrac{1}{{100}} \times \dfrac{{25}}{{10}}$
$ = \dfrac{{25}}{{1000}}$
This fraction can be written as decimal number as:
$ = 0.025$
This is because in the denominator we had three zeros; hence, we would shift the decimal point three digits towards the left.
Therefore,
$1\% $ of $1\% $ of $25\% $ of $1000 = 0.025$
Hence, option A is the correct answer.

Note: Instead of applying so many steps, we could just convert everything in one single step, i.e.
$1\% $ of $1\% $ of $25\% $ of $1000$
$ = \dfrac{1}{{100}} \times \dfrac{1}{{100}} \times \dfrac{{25}}{{100}} \times 1000$
Cancelling out the zeros we would get,
$ = \dfrac{1}{{10}} \times \dfrac{{25}}{{100}}$
Hence, this would give the same answer i.e. $0.025$
Also, we could have solved this question directly without using pen or paper by just a small trick.
Since, in the question everything is in multiplication and we have three $\% $ signs
And as we know that in one $\% $ sign we have $100$ i.e. $2$ zeros in the denominator.
Hence, three $\% $ signs would give us $2 \times 3 = 6$ zeros in the denominator.
Further, if we look at the numerator then we have a $1000$ i.e. $3$ zeros.
Hence, cancelling out, will leave us with a $25$ in the numerator and just $3$ zeros in the denominator.
Therefore, without using any pen or paper and just by our observation we would reach the second last step i.e.
$ = \dfrac{{25}}{{1000}}$
And simply convert it to its decimal form and reach our desired answer.