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Numbers that cannot be expressed as terminating or repeating decimals?
irrational numbers
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.
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 is an example of a terminating decimal?
A terminating decimal is a decimal number whose digits don't go on forever, like 3.45. A non-terminating decimal is a decimal number that goes on forever, like 1/3 = 0.3333333... since the 3's go on forever. So any repeating decimal is non-terminating. Also, numbers like pi go on forever: 3.1415926535897932384626.......
What are terminating and non terminating numbers in rational numbers?
Terminating numbers are decimal representations of rational numbers. Nonterminating numbers may or may not be rational numbers.
What numbers can be expressed as terminating or repeating decimal?
They are rational numbers
What can rational numbers be expressed as?
fractions or decimals
What are the irrational numbers?
Irrational numbers are numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.
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.
Can an irrational number be expressed as a terminating decimal?
No, irrational numbers can't be expressed as a terminating decimal.
What is a terminating and repeating decimal?
They are rational numbers.
Numbers that cannot be expressed as terminating or repeating decimals?
irrational numbers
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.
What is a decimal number that ends or recurs?
Decimal numbers that end or recur are known as terminating or repeating decimals. 0.75 is a terminating decimal. 0.4444 repeating is a repeating decimal.
What is the vocabulary for a terminating decimal and a repeating decimal?
They are both rational numbers.
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.
A repeating decimal is an irrational number?
Actually, a repeating decimal is not necessarily an irrational number. A repeating decimal is a decimal number that has a repeating pattern of digits after the decimal point. While some repeating decimals can be irrational, such as 0.1010010001..., others can be rational, like 0.3333... which is equal to 1/3. Irrational numbers are numbers that cannot be expressed as a simple fraction, and they have non-repeating, non-terminating decimal representations.
