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The value of x = 22/7: 2217 is a rational number then
How can I is an irrational number. .
aus.
Answers
Step-by-step explanation:
You don't really have to ask that! Look at 22/7. There it is. It is the ratio between 22 and 7. By definition a rational number.
It is very slightly confusing that rational also means reasonable. That suggests that numbers that cannot be written as the ratio of two integers, whole numbers, are not reasonable. That is what the school of Pythagoras thought of them when they proved that the square root of 2 cannot be written as a ratio of integers. They found irrational numbers didn't fit their concept of how maths should work. They, or their successors, called them surds. I think that is because they found them absurd.
As we learn more about numbers we may repeatedly have to allow our concept of number change. We start with the counting numbers. We add and go up. We subtract and go down. Then we discover we have gone down to zero. There's a new number, which caused some alarm a few hundred years ago. Then subtracting we go below zero and gave negative numbers.
Multiply and go up. Divide and you fall into gaps between integers. You are in the rational numbers.
By the way, we have not made any statements that depend on how we write our numbers yet. They could be Roman numerals like XXI or what we use now, called Arabic numerals, like 21.
Our rational numbers can have any integer as denominator but that makes add-in them difficult. So let's write our rational numbers as tenths+hundredths+thousandths, etc. 1/2 = 0.5, 3/2 = 1.5, 1/8=0.125. But 1/3=0.333333…. and 1/7=0.142857142857142857… without end. So our attempt to make the way we write rational numbers to help addition has got us into another complication.
Then we come to the surds and find we have stumbled on a whloe new field: the real numbers. Later we meet real numbers that aren't surds, transcendental numbers, including pi and e.
Go back to your algebra and find that a number has two square roots. 2 and -2 are both square roots of 4. But you equation may want to use the square root of -4 and you brain aches again. Can't exist? But it would be useful in alternating current theory. Lets use it but call it imaginary. So we are on the edge of complex numbers.
Be open minded about numbers. You can have horizons opening out a long way.