Rational numbers can be expressed as a terminating or repeating decimal.
Terminating or repeating decimal numbers.
Irrational numbers are numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.
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.
Any decimal that can't be expressed as a fraction is an irrational number
No, irrational numbers can't be expressed as a terminating decimal.
They are rational numbers.
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.
They are both rational numbers.
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.
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.
Repeating decimal. * * * * * It depends on the numbers! For example, 0.6 < 0.66... < 0.67 By the first inequality the repeatiing decimal is bigger, by the second the terminating one is bigger.
If you convert them into decimal form you can say there are terminating decimals, there are the integers, and there are repeating decimals. EX: 2.4 is a terminating decimal. 2.44444444... is a repeating decimal. 2 is an integer. all are rational numbers.
Because terminating or repeating decimals can be written as the quotient of two integers a/b, where b is not equal to zero.
Rational numbers can be written as a fraction with a non-zero denominator,as a terminating,a decimal,or a repeating decimal.
Terminating and repeating decimals are rational numbers.
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)
Yes, negative decimal numbers are rational, as long as it is terminating or repeating.
No. The simplest example is the number 1/3, which when expressed as a decimal is the infinite (non-terminating) 0.333...
No. Any number with a terminating or repeating decimal expansion is rational."Rational" in numbers means that it can be expressed as a ratio of integers (i.e. a fraction) .... in this case, -12/5.
It is a non-terminating, non-repeating decimal representation. That is a definition of irrational numbers.
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.
There are two kinds of decimals that are rational: terminating and repeating. Terminating decimals are simply decimals that end. For example, the numbers after the decimal point for 3.14, 5.5, and 424.827598273957 don't continue on forever; i.e. they terminate. Repeating decimals differ from terminating decimals in that the numbers after the decimal point continue on forever. For example, the numbers 3.333333333..., 10.010101010101..., and .0356811111111111..., where the "...'s" mean that the numbers continue on indefinitely, are all repeating decimals. The reason why both of these types of decimals are considered rational is because both types can also be expressed as a fraction of two integers. Non-repeating decimals, such as pi and the square root of two, can't be expressed as a fraction of two integers, and so therefore are irrational.
That is called an irrational number. Some of the most common irrational numbers are pi (3.14159....) and the square root of 2.
Yes, except that all irrational numbers will be non-terminating, non-repeating decimals.
A terminating number has a definitive value - A repeating number continues indefinitely. For example - 10 divided by 8 is 0.125 (a terminating number) - 10 divided by 3 is 3.333333 (the decimal repeats indefinitely).
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