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Number Systems

Short Answer Type

41. Write three numbers whose decimal expansions are non-terminating non-recurring.

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42. Find three different irrational numbers between the rational numbers

5 over 7

and

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43. Classify the following numbers as rational or irrational:

square root of 23

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44. Classify the following numbers as rational or irrational:

square root of 225

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45. Classify the following numbers as rational or irrational:

0.3796

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46. Classify the following numbers as rational or irrational:

7.478478......

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47. Classify the following numbers as rational or irrational:
1.101001000100001......

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48. Find two irrational numbers between 0.1 and 0.12.

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49. Find two irrational numbers between 2 and 2.5.

First Method
The two irrational numbers between 2 and 2.5 can be taken as
2.101001000100001......
and 2.201001000100001.......
Second Method
Note: If a and b are two distinct positive rational numbers such that ab is not a perfect square of a rational number, then $square root of ab$ is an irrational number lying between a and b.
∴ An irrational number between 2 and 2.5

$equals square root of 2 cross times left parenthesis 2.5 right parenthesis end root equals square root of 5$
Similarly, an irrational number between 2 and $square root of 5$

$equals square root of 2 square root of 5 end root$
∴ Two irrational numbers between 2 and 2.5 are $square root of 5$ and $square root of 2 square root of 5. end root$

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50.

Give two rational numbers lying between
0.232 332 333 2 3333 2...... and 0.212 112 111 2 1111......

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