Question

Express 0.235 in the form $\dfrac{p}{q}$, where p & q are integers & represent on the number line.

Answer 1

Hint: We are given a number in decimal representation; we need to convert it in $\dfrac{p}{q}$ form where p and q are integers. So we first multiply and divide the given number with n power of 10, where n is the number of digits after decimal place. Then we simplify it to the simplest form, and then represent it on the number line.

Complete step-by-step answer:
We are given the decimal number 0.235
Let us assume x be the given decimal.
$ \Rightarrow x = 0.235$
We know that the value of a number does not change when it is multiplied and divided by equal quantities. As there are three decimal places, we can multiply and divide the decimal with 1000.
$ \Rightarrow x = 0.235 \times \dfrac{{1000}}{{1000}}$
After the multiplication, we get
$ \Rightarrow x = \dfrac{{235}}{{1000}}$
We can see that 5 is a common factor of the numerator and denominator.
$ \Rightarrow x = \dfrac{{47}}{{200}}$
Therefore, the required form of the given number is $\dfrac{{47}}{{200}}$.

To represent it in a number line, we can draw a number line with 200 divisions between the numbers 0 and 1. Then the 47th division from 0 will be the required number. As we cannot draw all the 200 divisions between 0 and 1, we just show some divisions near the number we need to plot and then plot the number.


Note: The numbers of the form$\dfrac{p}{q}$, where p & q are integers are known as rational numbers. Even though it is not mentioned in the question, we must simplify the fraction such that there is no common factor other than 1 for the numerator and the denominator. A number line is the line which represents all the real numbers. Any real number can be plotted in a number line. For plotting the given number, we just represented a small portion inside the interval 0 and 1 as the number lies between zero and one. We have divided the line between 0 and 1 into 200 divisions and only some of the divisions are represented in the number line.