Question

9. (i). Insert an irrational number between 1/3 and 1/2​

Answer 1

Question:

Insert an irrational number between $\sf \dfrac {1}{3}$ and $\sf \dfrac {1}{2}$.

$\:$

Solution:

$\sf \dfrac {1}{3}$ = 0.333...

$\sf \dfrac {1}{2}$ = 0.5

☆ Irrational numbers are the numbers which can't be written in $\sf \dfrac {p}{q}$ form. They have non-terminating and non-repeating decimal expansions.

So, irrational numbers between $\sf \dfrac {1}{3}$ and $\sf \dfrac {1}{2}$ can be 0.365248094..., 0.45274777380..., 0.3874961172..., etc.

$\:$

Remember:

• Rational numbers have terminating or non-terminating and repeating decimal expansions. By terminating, we mean that the remainder becomes 0, and by non-terminating and repeating, we mean that the remainder never becomes 0, the numbers after decimals repeat themselves.
• Irrational numbers have non-terminating and non-repeating decimal expansions. Meaning that the remainder never becomes 0, and tge numbers after decimal don't repeat themselves.