write different between rational and irrational number
Answers
Answer:
Rational no. Can be written in the form of p/q.
Bit irrational no. Can not be written in the form pf p/q
◗ That is simple to state but not necessarily simple to understand.
The first numbers people used were the whole numbers (or “integers”), such as 1, 2, 3, 10096745, or -23.
Then when we needed to share out or measure quantities of things like rice, where it isn't practical to count the grains of rice, we do it by weight or volume, and then we need fractions such 1/2 or 3/4.
Out of the fractions grew the notion of rational numbers - numbers expressible in the form m/n where m and n are whole numbers. I say “expressible" in that form because they don't always appear that way.
For example the number 1.23 is a rational number because (obviously) it is 123/100.
In fact any number that you can write down with a finite number of digits before the decimal point and a finite number after it is a rational number.
But that still isn't quite the whole story because there are rational numbers that cannot be written down with a finite number of decimals. Clearly according to the definition 1/7 is a rational number but as a decimal it looks like this 0.142857 .. but then it continues 142857 again and again indefinitely. That is not saying something fundamental about the number 7 or 1/7 but only that 10 and 7 have no common factors.
Without going into all kinds of complicated mathematics, it turns out that although the decimal expansion of a rational number may carry on forever, it always repeats.
An irrational number when expressed as a decimal also must go on forever, but the sequence of digits never repeats.
Telling the difference when numbers are written down is therefore not a simple question, except that nobody can write down an irrational number exactly.
In a sense, they can't write down 1/7 as a decimal either without resorting to the trick of saying those digits 142857 “recurr”.
But the only way you can write down pi exactly is to name it (as I did then) or to write it as a symbol
....◗ _So I hope this answers your question without blinding you with all kinds of mathematical complications.