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Irrational Numbers
An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. While their existence was once kept secret from the public for philosophical reasons, they are now well accepted, yet still surprisingly hard to prove on an individual basis. Please post all questions about irrational numbers, including the famous examples of π, e, and √2, into this category.
3,962 Questions
Is the square root of 16 over 5 rational or irrational?
The square root of (any number that isn't a perfect square) is irrational.
Why in a rational number denominatior is not zero?
Division by 0 is not a valid mathematical operation - not just for rational numbers.
Why is 8 an accounting number and a rational number?
The positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. Thus d(30) =
number of such divisors=8, ľ(30) = sum of such divisors=72 and ľ2(30) =
sum of squares of such divisors= 1 + 4 + 9 + 25 + 100 + 225 + 900 = 1300.
From the formula, since 30=2.3.5, we have d(30 = (1 + 1)(1 + 1)(1 + 1) =
8; ľ(30 = 22
ˇ1
2ˇ1 : 32
ˇ1
3ˇ1 : 52
ˇ1
5ˇ1 = 3
1 : 8
2 : 24
4 = 72 and ľ2(30) = 24
ˇ1
22
ˇ1 : 34
ˇ1
32
ˇ1 : 54
ˇ1
52
ˇ1 =
15
3 : 80
8 : 624
24 = 5:10:26 = 1300.
Is 0.375932667 a rational or an irrational number?
0.375932667 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Is -0.8 a rational or irrational decimal?
-0.8 is a rational number because it can represented in the form of p/q (where p and q are integers).
-0.8 in the form of p/q: -8/10 or -16/20 or -80/100 etc.
Is the square root of 2 irrational or rational?
The square root of (any number that isn't a perfect square) is irrational.
No. It is a rational number. Since it can be expressed in the form p/q = 2/1 where 2,1 are integers.
Why does the keyboard have two sets of numbers?
For normal usage the conventional QWERTY keypad, with the number along the top is the most convenient. However, people who need to do a lot of numerical input prefer the numerical keypad.
Is 3333333 rational or irrational?
3333333 is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
Two is a rational number because it ends. If the number was 2.6769956387589653875832683836836823656596518..... then it would be irrational because it never ends.
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The definition of "rational number" is: "Any number that can be written as the ratio of two integers."
'2' can be written as 2/1, 4/2, 6/3, 8/4, 792/396, and a lot of other ratios of integers.
It satisfies the definition of "rational number". That makes it a rational number.
The answer given up above the broken line doesn't do it. It's true that the
decimal form of an irrational number never ends, but that fact can't be used
as a definition, because it doesn't work the other way. A decimal that never
ends is not necessarily an irrational number.
0.333333333... never-ending is the decimal representation of 1/3, which is
a perfectly good rational number.
