Question

find two rational number and two irrational number between 0.5 and 0.55​

Answer 1

What are two rational and two irrational numbers between 0.5 and 0.55?

0.50 & 0.55

The rationals between them are 0.51, 0.52, 0.53, 0.54. & irrationals between them are 0.505005000500005……………… & 0.51005100005100000510000000051……………………… (non terminating & non repeating decimals are irrational number

There are infinitely many of them.

I don’t think looking for rational numbers between 0.5 and 0.55 is an issue. Any two numbers that you can write with finitely many digits after the decimal point will suffice.

Just to make this more worth our while, let us look for two rational numbers between 0.5 and 0.55 such that the four numbers are equally spaced.

Find the common constant difference (the equal spacing) first.

d=0.55−0.53

⟹d=0.053

The two numbers will then be 0.5+d and 0.5+2d.

0.5+d=0.5+0.053

⟹0.5+d=1.553=0.516¯¯¯

0.5+2d=0.5+2×0.053

⟹0.5+2d=1.63=0.53¯¯¯

Two irrational numbers can simply be written as the sum of a number known to be irrational and some rational number. For instance, π−2.6 and π−2.61 can be the answers.

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Answer 2

Answer: check the attachment

Step-by-step explanation:

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