Math and Arithmetic

# Is 10 times pi rational?

012 ###### 2017-09-17 14:20:15

No because the value of pi as regards to a circle is an irrational number

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## Related Questions No 10*pi is not a rational number because it can't be expressed as a fraction  No because 15 times pi is an irrational number No; since pi is irrational if you multiply it by a rational number it is still irrational It the radius is r then the area is pi*r*r - which is pi times a rational number. pi is an irrational number, so the multiple of pi and a rational number is irrational. Any multiple of or addition to or subtraction from PI is an irrational number. PI divided by PI is 1, a rational number. So is PI times 0 = 0 3 times pi is an irrational number because it can't be expressed as a fraction A non-zero rational number (10) multiplied by an irrational number (pi) is always irrational. e^pi ~ 23.14069.............., not rational 3.14 is a rational number pi is not. pi is not 3.14 Pi is not rational it is irrational because it does not stop or repeat (pi) itself is an irrational number. The only multiples of it that can be rational are (pi) x (a rational number/pi) . I assume you mean 2 times pi. Since pi is irrational, 2 pi is also irrational. Any number times pi is irrational. If you mean 0.3 times pi then it is an irrational number No because it can't be expessed as a fraction Yes. 2 x 3.14 = 6.28 = 6 7/25 = 157/25 which is rational. If you are using 3.14 as an approximation to {pi}, then 2 x {pi} is not rational.   Yes. For example: a = 10 - pi b = pi Both are irrational; the sum a + b is 10. Assuming that you mean pi, and not pie, it is not a rational number.The set of rational numbers is a field and this means that for every non-zero rational number, there exists a multiplicative inverse in the setand also, due to closure, the product of any two rational numbers is a rational number.Now suppose 7*pi were rational.7 is rational and so there is its multiplicative inverse, which is (1/7).(1/7) is also rational so (1/7)*(7*pi) is rationalBut by the associative property, this is (1/7*7)*pi = 1*pi = pi.But it has been proven that pi is irrational. Therefore the supposition must be wrong ie 7*pi is not rational. Sure; for example, 10 + pi is irrational, 10 - pi is irrational. Both are positive. If you add them, you get 20. The product of two rational numbers, as in this example, is always RATIONAL.However, if you mean 10 x pi, pi is irrational; the product of a rational and an irrational number is ALWAYS IRRATIONAL, except for the special case in which the rational number is zero. Yes. For example, if you take any truncated equivalent of pi then it will be rational. You may or may not be able to. The diameter of a circle with circumference 10 cm is 10/pi, a division problem. But there is no answer using rational numbers.

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