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Find two rational and two irrational numbers between 0.5 and 0

Question

Find two rational and two irrational numbers between $0.5$ and $0.55$ .

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Find two rational and two irrational numbers between

0.5

and

0.55

12 mins ago

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12 mins ago

Text solutionVerified

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}

On further calculation

= \frac{1.5 + 0.05}{3}

and

\frac{1.5 + 0.1}{3}

So we get

= \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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Question Text	Find two rational and two irrational numbers between $0.5$ and $0.55$ .
Answer Type	Text solution:1
Upvotes	155

Find two rational and two irrational numbers between 0.5 and 0.55.

Text solutionVerified

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Find two rational and two irrational numbers between $0.5$ and $0.55$ .