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What numbers can be expressed as a terminating or repeating decimal?
Rational numbers can be expressed as a terminating or repeating decimal.
Are decimals in a fraction always rational numbers?
There are are three types of decimals: terminating, repeating and non-terminating/non-repeating. The first two are rational, the third is not.
What is a counterexample to show that the repeating decimals are closed under subtraction false?
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.
Why are terminating decimals rational numbers?
they always are.
A repeating decimal is a real number?
Yes repeating decimals are real numbers. They can fall under the category of rational numbers under real numbers since their repeating decimal patterns allows them to be converted into a fraction. Nonreal numbers are imaginary numbers which are expressed with i, or sqrt(-1).
What can rational numbers be expressed as?
fractions or decimals
Are terminating and repeating decimals irrational numbers?
Terminating and repeating decimals are rational numbers.
What numbers can be expressed as a terminating or repeating decimal?
Rational numbers can be expressed as a terminating or repeating decimal.
What are terminating and repeating decimals?
Irrational Numbers.
What are two characteristics of a rational and irrational number?
Rational numbers - can be expressed as a fraction, and can be terminating and repeating decimals. Irrational numbers - can't be turned into fractions, and are non-repeating and non-terminating. (like pi)
Is 0.313131 a rational number?
Yes, it is a repeating decimal. Terminating and repeating decimals are rationals. Rational numbers can also be expressed as a fraction. 0.313131 is a repeating decimal.
What type of decimals are irrational numbers?
Non-terminating, non-repeating decimals.
Are all terminating and repeating decimals rational numbers and why?
Yes, they are and that is because any terminating or repeating decimal can be expressed in the form of a ratio, p/q where p and q are integers and q is non-zero.
Are decimals in a fraction always rational numbers?
There are are three types of decimals: terminating, repeating and non-terminating/non-repeating. The first two are rational, the third is not.
What are non-repeating and non-terminating decimals?
Irrational Numbers.
Is 23.8282828282 irrational?
No. Numbers with terminating or repeating decimals are rational.
What numbers can be expressed as terminating or repeating decimal?
They are rational numbers
