500 hundred digits and the 27th is 8
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If you mean the number pi, you can't have a "large amount of pi" or a "small amount of pi" - the number pi will always be the number pi (approximately 3.1416).
we can find rational numbers how much nearer to pi by constructing a number which has large repeating block as pi
No. Infinity goes on forever, and thus is an 'infinitely' large number. Pi however, even though it has infinite decimal places, will never be a bigger number than what it is. By this I mean Pi can never be measured as 3.2. Or 3.15. Or 3.143. At least in my understanding.
An approximation of pi is 3.14159568. It is a non-repeating decimal, and many powerful computers have calculated trillions of decimal places, so the known number is too large for this space.
pi is a transcendental number, which is a kind of irrational number. As a result it cannot have a fractional form. A convenient approximate fraction is 22/7 so that pi/2 would be approx 11/7 (which is about 0.04% too large).