Must a rational number be rational?
Yes, if it wasn't it wouldn't be a rational number.
Yes, it must.
Which number can be multiplied to a rational number to explain that the product of two rational numbers is rational?
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
The sum of a rational and irrational number must be an irrational number.
No number can be both rational and irrational. And, at the level that you must be for you to need to ask that question, a number must be either rational or irrational (ie not neither). 0.555555 is rational.
Yes. In fact, it MUST BE rational.
No. In fact the sum of a rational and an irrational MUST be irrational.
No, a rational number must be a whole number, for example 40 and 5643 and 948.
nope. rational numbers must be positive.
Let R + S = T, and suppose that T is a rational number. The set of rational number is a group. This implies that since R is rational, -R is rational [invertibility]. Then, since T and -R are rational, T - R must be rational [closure]. But T - R = S which implies that S is rational. That contradicts the fact that y is an irrational number. The contradiction implies that the assumption… Read More
Since it has a terminating decimal (or binary or to any other rational base) representation, it must be rational.
Not all real numbers are rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
To be a rational number, it must be able to be expressed as a fraction(i.e., p/q) where q is any number except zero (it can be 1). Your number can be expressed as 5232323232323232323/1000000000000000000 So it is rational.
Not necessarily. 1/3 + 1/3 = 2/3 which is (must be) rational, but is not a natural number.
Let A be a non-zero rational number and B be an irrational number and let A*B = C.Suppose their product C, is rational. Then, dividing both sides of the equation by A gives B = A/C. Now, since A and C are both rational, A/C must be rational. Therefore you have B (irrational) = A/C (irrational). Clearly, this is impossible and therefore the supposition must be wrong. That is to say, A*B cannot be ration… Read More
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.
Yes. Any number that is not rational would not be called 'rational', and so it would not be included in the bag of 'rational numbers'. So all the numbers that are in there must be rational ones.
from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that… Read More
It is due to the fact that the set of real numbers is defined as the union of the rational and irrational numbers.
Suppose x is a rational number and y is an irrational number. Let x + y = z, and assume that z is a rational number. The set of rational number is a group. This implies that since x is rational, -x is rational [invertibility]. Then, since z and -x are rational, z - x must be rational [closure]. But z - x = y which implies that y is rational. That contradicts the fact… Read More
What is true of the discriminant when the two real number solutions to a quadratic equation are rational numbers?
The discriminant must be a perfect square or a square of a rational number.
Yes. Any number which can be written down to all its places exactly is rational. A proviso is that the base (most commonly base 2 or base 10) must also be rational. Any number which is the ratio of two rational numbers (such as 1/3, or 186/100) is rational.
NO it is not a square root, sqrt 44 = 6.6. It must be equal to be rational.
No. To be a rational number it must be an integer over another integer. π is not an integer, nor can it be made into an integer by multiplying it by another integer, thus one twelfth of π is not a rational number.
Not always because any number that can be expressed as a fraction is a rational number as for example 0.666...recurring can be expressed as 2/3 as a fraction
because it can be written as a fraction. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
The set of real numbers is divided into rational and irrational numbers. The two subsets are disjoint and exhaustive. That is to say, there is no real number which is both rational and irrational. Also, any real number must be rational or irrational.
It is not easy. If the value is rational then you must be able to express the value under the radical sign as p2/q2 where p and q are integers and q is non-zero. If not, then the number is irrational. It is not enough to require that for a rational, the number under the radical must be a perfect square since sqrt(2.25) is rational even though 2.25 is not a perfect square.
In a group with closure the solution to the operation must be a number from the same set. The set of integers and the set of rational numbers are closed under addition. So the sum of two (or more) integers must be an integer, the sum of rational numbers must be a rational number.
The sum of a rational and an irrational number is always irrational. Here is a brief proof: Let a be a rational number and b be an irrational number, and c = a + b their sum. By way of contradiction, suppose c is also rational. Then we can write b = c - a. But since c and a are both rational, so is their difference, and this means that b is rational as… Read More
Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction. You must make sure it can be written as a fraction.
Those are the rational numbers. To be precise, you must be able to write the number as a fraction, with integers in the numerator and the denominator, to qualify as a rational number.
The numerator must be an even number and the denominator is half of the numerator.
Integers are a subset of rationals, so 360 is a rational. If you must express it as a ratio, the simplest is 360/1.
The additive opposite of the rational number q is -q. One of q and -q must be non-negative and that is its absolute value.
A rational number. A rational number. A rational number. A rational number.
All finite numbers are rational. A rational number is any number that can be expressed as one integer divided by another. 0.725 is clearly rational because it can be expressed straight off as 725/1000. Even though that isn't the simplest fraction to mean 0.725, it is enough to show that 0.725 must be rational.
The decimal expansion of a rational number always either terminates after finitely many digits or begins to repeat the same finite sequence of digits over and over. As 7.37 terminates after 2 digits it must therefore be rational.
There are rational numbers and irrational numbers. Real numbers are DEFINED as the union of the set of all rational numbers and the set of all irrational numbers. Consequently, all rationals, by definition, must be real numbers.
Yes, for example, square root of 2 x square root of 2 = 2. * * * * * No, the product of two rational numbers must always be rational. No. Proof : If you take rational number a/b and multiply by rational c/d you get ac/bd. Since ac and bd are each integral, the product is rational.
Let x be a rational number and y be an irrational number.Suppose their sum = z, is rational. That is x + y = z Then y = z - x The set of rational number is closed under addition (and subtraction). Therefore, z - x is rational. Thus you have left hand side (irrational) = right hand side (rational) which is a contradiction. Therefore, by reducio ad absurdum, the supposition that z is rational… Read More
A rational number is a number that can be expressed as a/b. a and b must both be integers. For any finite decimal, you can multiply by a power of 10 to get an integer. In this case, you can multiply by 1,000 to get 682. Therefore, 0.682 can be expressed as 682/1,000. This is why 0.682 is rational.
I assume you mean that the sequence continues this way. No, it is not. To be rational, the same pattern - excatly the same sequence of digits - must repeat over and over, since any fraction (i.e., rational number) converted to decimal has this type of pattern.
An irrational number is a number that cannot be expressed as a/b. a and b must both be integers. With 56, this can be expressed as 56/1. As both 56 and 1 are integers, 56 is a rational number. All whole numbers are rational.
Twice the rational number 5/2 = 5From this, you need to subtract 4 3/5 to get 2/5.
you mean is a whole number a rational number? and yes it is and rational number. Any number that can be put in a fraction is a rational number
It is a set containing the single number, 3.14, a rational number. This must not be confused with the number pi, which is approximately 3.14 but is an irrational number.
There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.
Certainly. Otherwise, there would be a rational number whose square was an irrational number; that is not possible. To show this, let p/q be any rational number, where p and q are integers. Then, the square of p/q is (p^2)/(q^2). Since p^2 and q^2 must both be integers, their quotient is, by definition, a rational number. Thus, the square of every rational number is itself rational.
As much as, in these days of uncertainty, anything can be anything. As long as the constraints of a rational number are kept to, a rational number will always remain a rational number.