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Which property would be useful in proving that the product of two rational numbers is always rational?
The fact that the set of rational numbers is a mathematical Group.
Are rational numbers under addition a group?
Yes.
Why does every rational number have a additive inverse?
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
how do you find out if a decimal is rational?
If a decimal can be expressed as a fraction then it is a rational number as for example 0.75 = 3/4 Also, if the decimal ever ends, or is a never ending repeat of the same digit or group of them, then it's a rational number.
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Is 2.3333..... irrational or rational?
It is rational.Any number that has a digit, or group of digits, that repeat forever is rational.
What is a group of rational numbers?
A rational number is a number that can be expressed in fractional form.
Which property would be useful in proving that the product of two rational numbers is always rational?
The fact that the set of rational numbers is a mathematical Group.
Are rational numbers under addition a group?
Yes.
Why does every rational number have a additive inverse?
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
Is the set of rational numbers a commutative group under the operation of division?
No, it is not.
Is this a rational number 0.131131113?
If you mean to continue the pattern indefinitely, adding more digits, and one more "1" in every cycle, then it is NOT rational. In the case of a rational number, the EXACT SAME group of digits has to repeat over and over (perhaps after some other, initial, digits), for example:0.45113113113113113... Here, the group of digits "113" repeats over and over, so the number is rational.
how do you find out if a decimal is rational?
If a decimal can be expressed as a fraction then it is a rational number as for example 0.75 = 3/4 Also, if the decimal ever ends, or is a never ending repeat of the same digit or group of them, then it's a rational number.
Is rational number is a cyclic group under addition?
No Q is not cyclic under addition.
Rational and irrational numbers make up what group?
They make up the Real numbers.
Do positive rational numbers form group?
Yes, with respect to multiplication but not with respect to addition.
Why are the rational numbers under the operation of multiplication not a group?
I believe it is because 0 does not have an inverse element.
