Question

Express 0.001 in the form of $\dfrac{p}{q}$.

Answer 1

Hint:
We will take a variable x and assign it to the value given in the question, then we will multiply x with a power of 10 such that the fraction assign to the variable x becomes an integer then we will divide both side by the power of 10 that we have just multiplied and then we will get the required form of $\dfrac{p}{q}$ .

Complete step by step solution:
There are two types of decimal expansion of numbers
1. Finite decimal expansion - where the decimal part of the fraction is finite, in this question the value given is in finite decimal expansion. for example, 0.203,0.34.
2. Infinite decimal expansion – Where the decimal part of the fraction is infinite, for example 0.55…
0.001 is of finite decimal expansion
Let us assign a variable x to the value 0.001, so
 $ \Rightarrow x = \;0.001$
Then we will multiply x with a power of 10 such that the fraction assigned to the variable x becomes an integer.
 $ \Rightarrow \;x \times \;1000 = 1$
On dividing the equation by 1000, we get,
 \[ \Rightarrow x = \dfrac{1}{{1000}}\] which is in $\dfrac{p}{q}$ form where $p = 1$ and $q = 1000.$

So $\dfrac{p}{q}$ form of 0.001 is $\dfrac{1}{{1000}}$.

Note:
Sometimes the fraction will come repeating, consider in the case of 0.555… then in that case we will assign a variable to that decimal expansion and multiply both side with a power of 10 such that the multiplication puts the decimal sign just after the repetition begins, then we will simplify to get the value of the variable which will be in $\dfrac{p}{q}$ form.