Question
Find two rational and two irrrational numbers between $0.5$ and $0.55.$
✓
Answer
We know that, $0.5<0.55$
Consider $x =0.5, y =0.55$ and $n =2$
$d=\frac{y-x}{n+1}=\frac{0.55-0.5}{2+1}=\frac{0.05}{3}$
Two rational and two irrational numbers which lies between $0.5$ and $0.55$ are $x + d$ and $x +2 d$
so we get,
$=0.5+\frac{0.05}{3}$ and $0.5+2 \times \frac{0.05}{3}$
$=\frac{1.5+0.05}{3}$ and$\frac{1.5+0.1}{3}$
$=\frac{1.55}{3}$ and $\frac{1.6}{3}$
By division
$= 0.51$ and $0.53$
Two irrational numbers which lies between $0.5$ and $0.55$ are $0.5151151115 ....$ And $0.5353553555$
Consider $x =0.5, y =0.55$ and $n =2$
$d=\frac{y-x}{n+1}=\frac{0.55-0.5}{2+1}=\frac{0.05}{3}$
Two rational and two irrational numbers which lies between $0.5$ and $0.55$ are $x + d$ and $x +2 d$
so we get,
$=0.5+\frac{0.05}{3}$ and $0.5+2 \times \frac{0.05}{3}$
$=\frac{1.5+0.05}{3}$ and$\frac{1.5+0.1}{3}$
$=\frac{1.55}{3}$ and $\frac{1.6}{3}$
By division
$= 0.51$ and $0.53$
Two irrational numbers which lies between $0.5$ and $0.55$ are $0.5151151115 ....$ And $0.5353553555$
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