Finding irrational numbers between two numbers — lesson. Mathematics State Board, Class 9.

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எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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Steps to find the irrational numbers between two numbers:

Step 1: Express the provided number in decimal form.

Step 2: Keep in mind that we need to construct irrational numbers between the provided numbers.

Step 3: Within the possible range construct irrational numbers such that they are non-recurring and non-terminating.

Example:

Consider two numbers

$1/6$ and

$2/3$ .

The decimal expressions of provided numbers are

$1/6 = 0.1666...$ and

$2/3 = 0.6666...$

Now we have to construct irrational between

$0.1666...$ and

$0.6666...$

Remember that irrationals are non-recurring and non-terminating.

We ourself can construct numbers with the given conditions.

Let the numbers are

$0.17070070007....$ ,

$0.23003000300003...$ ,

$0.35010011011101111...$

In this way, we can construct an infinite number of irrationals between any two numbers.

The easiest way to express an irrational number between two rational numbers:

Step 1: Express the smaller rational number as a terminating decimal.

Step 2: Put

$01$ after its last decimal.

Step 3: Then put

$001$ then put

$0001$ then put

$00001$ … … … so on and on.

Step 4: Hence the resultant number is an irrational number between the two given rational numbers.

Example:

Consider the same two numbers

$1/6$ and

$2/3$ .

The decimal expressions of provided numbers are

$1/6 = 0.1666...$ and

$2/3 = 0.6666...$

Now we have to construct irrational between

$0.1666...$ and

$0.6666...$

Let us round off the smallest rational number to three decimal places.

Thus, the smallest rational number is

$0.167$ .

Now add the number

$01$ , it becomes

$0.16701$ .

Then add

$001$ ,

$0.16701001$ .

Now add

$0001$ ,

$0.167010010001$

Then add

$00001$ ,

$0.16701001000100001$ .

Proceeding in the same way, the number becomes as follows:

$0.16701001000100001000001...$

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8. Finding irrational numbers between two numbers

Theory: