# Number Systems

## Class 9 NCERT Maths

### NCERT

1   Is zero a rational number? Can you write it in the form $\dfrac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$?

Consider the definition of a rational number.$\\$ A rational number is the one that can be written in the form of $\dfrac{p}{q}$ where $p$ and $q$ are integers and $q\neq 0$$\\ \bullet Zero can be written as \dfrac{0}{1},\dfrac{0}{2},\dfrac{0}{3},\dfrac{0}{4},\dfrac{0}{5}....$$\\$ $\bullet$ Zero can be written as well$\dfrac{0}{-1},\dfrac{0}{-2},\dfrac{0}{-3},\dfrac{0}{-4},\dfrac{0}{-5}....$$\\ So, we arrive at the conclusion that 0 can be written in the form of \dfrac{p}{q} Where p and q are integers ( q can be positive or negative integers).\\ Therefore, zero is a rational number. 2 Find six rational numbers between 3 and 4. ##### Solution : We know that there are infinite rational numbers between any two numbers. As we have to find 6 rational numbers between 3 and 4 So multiply and divide by 7 (or any number greater than 6)\\ We get,3=3*\dfrac{7}{7}=\dfrac{21}{7}\\ 4=4*\dfrac{7}{7}=\dfrac{28}{7}$$\\$ Thus the $6$ rational numbers are $\\$ $\dfrac{22}{7},\dfrac{23}{7},\dfrac{24}{7},\dfrac{25}{7},\dfrac{26}{7},\dfrac{28}{7}$

3   Find five rational numbers between $\dfrac{3}{5}$ and $\dfrac{4}{5}$