Question

What is \[0.04\% \] into a fraction?

Answer 1

Hint: As we have to convert the percentage into the fraction number, first we will divide the percentage by \[100\] and remove the percent sign. Now to convert it into a fraction, just drop the decimal point and divide the term by \[{10^x}\] where \[x\] will be the number of digits on the right side of the decimal point. In this case, as we have two numbers after the decimal point, we will divide by \[100\] and then reduce the above fraction to its simplest form to get the result.

Complete step-by-step answer:
We are provided with a percentage, according to the given question, which we have to turn into a fraction. Here, we are given a \[0.04\% \] figure.
Now, to turn a percentage into fraction first we will divide the percentage by \[100\] and remove the percent sign.
So, \[0.04\% \] can be written as \[\dfrac{{0.04}}{{100}}\]
Now, to convert it into a fraction, we have to just drop the decimal and divide the term by \[{10^x}\] where \[x\] will be the number of digits on the right side of the decimal point to convert into fraction
Here, we have two numbers after the decimal point, so we will drop the decimal point and divide by \[100\]
Therefore, we get
\[\dfrac{{004}}{{100 \times 100}}\]
This can also be written as,
\[\dfrac{4}{{10000}}\]
Now, we will reduce the above fraction to its simplest form
So, \[\dfrac{4}{{10000}}\] can be written as, \[\dfrac{4}{{{{\left( {10} \right)}^4}}}\]
As we know, \[10 = 2 \times 5\]
So, we can also write it as, \[\dfrac{4}{{{{\left( {2 \times 5} \right)}^4}}}\]
We know that \[{\left( {a \times b} \right)^m} = {a^m} \times {b^m}\]
Therefore, the above fraction becomes, \[\dfrac{4}{{{2^4} \times {5^4}}}\]
\[ = \dfrac{4}{{4 \times {2^2} \times {5^4}}}\]
On cancelling we get,
\[ = \dfrac{1}{{{2^2} \times {5^4}}}\]
\[ = \dfrac{1}{{4 \times 625}} = \dfrac{1}{{2500}}\]
which is the required result.
Hence, the value of \[0.04\% \] into a fraction is \[\dfrac{1}{{2500}}\]
So, the correct answer is “\[\dfrac{1}{{2500}}\]”.

Note: Whenever we come up with this type of problem, always remember that when a fraction is reduced to its simplest form, it cannot be reduced further, if it is reduced further then it needs to be checked again. Also, while doing calculations just try to make the denominator as base \[10\] to make the calculations easier. Like in this question, we have a smaller number of terms in the denominator, so we just multiply them manually, but it can also be done by making denominator as base \[10\]
Like in the above calculation when we get the fraction after cancelling i.e.,
\[ = \dfrac{1}{{{2^2} \times {5^4}}}\]
\[ = \dfrac{1}{{{2^2} \times {5^2} \times {5^2}}}\]
Now to make denominator \[10\] we can write it as,
\[ = \dfrac{1}{{\left( {{2^2} \times {5^2}} \right) \times {5^2}}} = \dfrac{1}{{{{\left( {2 \times 5} \right)}^2} \times {5^2}}}\]
\[ = \dfrac{1}{{{{\left( {10} \right)}^2} \times {5^2}}} = \dfrac{1}{{100 \times 25}} = \dfrac{1}{{2500}}\]
Hence, we get our required result.