Question

While representing $\dfrac{2}{3}$ on a number line, between which two integers does the point lie?
A) 1 and 2
B) 0 and 1
C) 2 and 3
D) 1 and 3

Answer 1

Hint: To solve this question we need to know to represent a number in a number line, especially a fraction. The step to represent the fraction in the number line is to convert the fraction into a decimal number and then check the number prior or left to the decimal point.

Complete step by step answer:
The question asks us to find the two points between which the number $\dfrac{2}{3}$ is represented in the number line. So the first step in this process is to convert the fraction number $\dfrac{2}{3}$ into a decimal form. On doing this we get the decimal number we get is:
$\Rightarrow \dfrac{2}{3}$
The fraction is converted into decimal by dividing the numerator with the denominator. In this case $2$ is divided by $3$ which gives the result as:
$\Rightarrow 0.67$
The second step is to analyse the decimal number. We see that in the one’s place of the decimal number we have $0$ which means the number given to us lies between $0$and $1$. This is shown in the number line given below, where point A is the point representing the fraction $\dfrac{2}{3}$ or $0.67$.

$\therefore $ The number $\dfrac{2}{3}$ when represented on the number line lies between option B) $0$ and $1$.

Note: The fraction without converting into decimal can also be represented in the number line. In case of a proper fraction which means the fraction is less than$1$, the fraction will always lie between $0$ and $1$. Since in this question the fraction $\dfrac{2}{3}$ is a proper fraction which means the numerator is smaller than the denominator so the fraction here will lie between $0$ and $1$in the number line.