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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.
Is 9.55 a rational number?
Yes
If a non-terminating decimal that is not a fraction is called irrational what do you call a non-terminating decimal that is a ratio of rational numbers such as 1 over 7?
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.
What numbers can be expressed as a terminating or repeating decimal?
Rational numbers can be expressed as a terminating or repeating decimal.
Why are terminating decimals rational numbers?
they always are.
Are rational numbers non-terminating decimals?
No. Rational numbers are either terminating decimals or non-terminating BUT recurrent decimals.
Are non-terminating decimals rational numbers?
If they are non-terminating and there is a repeating pattern, then they are rational. If they are non-terminating and there is no repeating pattern, as in pi, they are irrational.
Is an irrational a non-terminating decimal?
Not only non-terminating, but also non-repeating. 0.333... recurring is non-terminating but it is rational. In fact, most rational numbers are non-terminating decimals.
Are irrational numbers always non-terminating?
Yes. Any terminating number is rational. (But some non-terminating numbers are rational too, like 1/3, 1/7, 1/9, etc.
What are non-terminating numbers?
They are real numbers. All irrational numbers are non-terminating. Also, any rational numbers which, in its simplest form has a denominator which contains a factor other than 2 or 5 (or their powers) is non-terminating.
Why is 8.3 a rational number?
It terminates. I believe that numbers that are non terminating are irrational. and numbers that can be made into a fraction, terminat, or repeat are rational.
Are terminating decimals always rational numbers?
Yes, terminating decimals are always rational numbers.
Is non-terminating decimal is a rational or irrational number?
Either. If it is non-terminating but recurrent (after some point) it is rational. If it is non-terminating AND non-recurrent then it is irrational.
Are rational numbers non terminating decimals?
They can be. For example, 3/11 = 0.272727... recurring forever.
Are terminating and repeating decimals irrational numbers?
Terminating and repeating decimals are rational numbers.
Is every rational number a decimal number?
All real numbers have a decimal representation. Rational numbers have decimal representations that terminate or repeat infinitely. Irrational numbers have decimal representations that are non-terminating and non-repeating.
If a non-terminating decimal that is not a fraction is called irrational what do you call a non-terminating decimal that is a ratio of rational numbers such as 1 over 7?
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.
