Q: The terminating decimals are closed under division?

Write your answer...

Submit

Still have questions?

Continue Learning about Math & Arithmetic

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

There cannot be a counterexample since the assertion is true. This requires you to accept the true fact that the terminating decimal 1.25, for example, is equivalent to the repeating decimal 1.25000... (or even 1.24999.... ).

no

The whole numbers are not closed under division! The statement is false since, for example, 2/3 is not a whole number.

No, it is not. Division by zero (a rational) is not defined.

Related questions

no, but is a hard question 4 some 1 like me who is young....... thanks 4 asking! (:

Division by 0, which can also be written as 0.000... (repeating) is not defined.

Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.

They are closed under all except that division by zero is not defined.

In fact, the statement is true. Consequently, there is not a proper counterexample. The fallacy is in asserting that a terminating decimal is not a repeating decimal. First, there is the trivial argument that any terminating decimal can be written with a repeating string of trailing zeros. But, Cantor or Dedekind (I can't remember which) proved that any terminating decimal can also be expressed as a repeating decimal. For example, 2.35 can be written as 2.3499... Or 150,000 as 149,999.99... Thus, a terminating decimal becomes a recurring decimal. As a consequence, all real numbers can be expressed as infinite decimals. And that proves closure under addition.

There cannot be a counterexample since the assertion is true. This requires you to accept the true fact that the terminating decimal 1.25, for example, is equivalent to the repeating decimal 1.25000... (or even 1.24999.... ).

It is called a rational number. The rational numbers are closed under the operations of addition, subtraction, multiplication, and division (not dividing by 0). The fact that it is not terminating is not important at all. In fact, if we use other bases besides base 10, we will see that the set of numbers that are rational or irrational doesn't change. However, if we use another base, for example base 3, then the number 1/3 in base 3 can be represented with a terminating "decimal" (technically not decimal). The set of rational numbers that have terminating "decimals" depends on the base.

No, they are not.

No.

no

No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.

yes