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Is the statement A terminating decimal cannot be expressed as a repeating decimal false?
Wiki User
∙ 11y ago
Yes.
5.0 (a terminating decimal) can be expressed as 4.9999... (a repeating decimal)
That may be hard to believe but it is true, as proved by Georg Cantor.
Wiki User
∙ 11y ago
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When expressed as a decimals rational number will be what or repeating?
When expressed as a decimal, a rational number will either be terminating (end with a finite number of digits) or repeating (have a repeating pattern of digits).
Who of the following cannot be written as a fraction an integer a terminating decimal a repeating decimal and a non-terminating non repeating decimal?
The latter which would be an irrational number that cannot be expressed as a fraction.
Does the sum of a repeating decimal and a terminating decimal equal a terminating decimal?
No, the sum of a repeating decimal and a terminating decimal is never a terminating decimal.
What is a decimal called when it is not a repeating or terminating number?
Any decimal that can't be expressed as a fraction is an irrational number
A number that connot be expressed as a ratio of two integers or as a repeating or terminating decimal?
Irrational.
What numbers can be expressed as a terminating or repeating decimal?
Rational numbers can be expressed as a terminating or repeating decimal.
What numbers can be expressed as terminating or repeating decimal?
They are rational numbers
When expressed as a decimals rational number will be what or repeating?
When expressed as a decimal, a rational number will either be terminating (end with a finite number of digits) or repeating (have a repeating pattern of digits).
How do you determine whether you can write a given decimal as a fraction?
If the decimal is terminating or repeating then it can be written as a fraction. Decimal representations which are non-terminating and non-repeating cannot be expressed as a fraction.
What is a number that cannot be expressed as a repeating or terminating decimal?
An irrational number.
Who of the following cannot be written as a fraction an integer a terminating decimal a repeating decimal and a non-terminating non repeating decimal?
The latter which would be an irrational number that cannot be expressed as a fraction.
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.
Does the sum of a repeating decimal and a terminating decimal equal a terminating decimal?
No, the sum of a repeating decimal and a terminating decimal is never a terminating decimal.
What can rational numbers be expressed as?
fractions or decimals
Is 0.66 a terminating or repeating decimal?
It is terminating - after two decimal digits.
What is a decimal called when it is not a repeating or terminating number?
Any decimal that can't be expressed as a fraction is an irrational number
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.
