Can a circle have a rational circumference?

The fact that Pi is irrational means that you can’t have a circle with both the circumference and diameter being integers. In fact you can’t even have the circumference and diameter both rational since the quotient of two rationals is again a rational. “Ratios” of lengths can yield other irrational numbers also.

Can the diameter of a circle and the circumference of the same circle both be rational numbers?

If you are asking if a circle can have both a rational diameter and a rational circumference, then no they cannot both be rational in the same units.

Is the circumference of a circle always an irrational number?

If π is irrational and D rational, then C is irrational. If it were rational, then C/D=π would be rational. “Turning the argument around”: We know, that the circumference of a circle with rational diameter is always irrational. Therefore C/D=π is irrational.

Is radius rational or irrational?

Now for a given radius r of a circle we can have following cases: Case 1: r is a rational number(>0). In this case the area of a circle will ALWAYS be irrational, since π is irrational and r2 always rational.

Is 7.787887888 a rational or irrational number?

Yes; it has a pattern which is repeating.

Do you think there can be some numbers that are not rational numbers?

Answer: Yes, there are numbers which are not rational (can’t be rewritten as a fraction with integers ) they are called ir rational numbers. Hope it helps you.

Can the diameter of a circle be irrational?

Either the circumference or the diameter of a circle will be irrational because and is irrational. If you take a rational number and multiply it or divide it by an irrational number then you get an irrational number. “Irrational” means that it’s not the ratio of two integers.

Is the diagonal of a square irrational?

‘The diagonal of a square is irrational’ This statement is sometimes true. If the sides of the square are 2 units long, then the diagonal is 22 +22 = 4+ 4 = 8 which is irrational.

Can the area of a circle be an integer?

If you allow any radius for a circle, then a circle has integer area if and only if its radius r is the square root of an integer divided by π, that is, r=√a/π for some nonnegative integer a.