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pi is an irrational number. It can not be expressed as a ratio of two integers.
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).
It depends on if it is continued or not. A terminal decimal is always rational (such as 0.5) If it has a repeating pattern, its also rational (0.3333333333333333). If you mean 0.50550555055550555550555555 etc.) this is not rational.
No An irrational number goes on forever with no repeating pattern.
A non-terminating decimal is a decimal that does not terminate, and goes on forever, and a repeating decimal is a number that continues on forever with a repeated pattern
Correct -
No. If the decimal expansion falls into a repeating pattern (however long) then the number is rational. For example, 0.33... is the rational number 1/3. or 0.04142857142857... where the pattern 142857 continues forever is the rational number 29/700.
True
pi is an irrational number. It can not be expressed as a ratio of two integers.
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.
Repeating decimals are rational numbers if there is a pattern, like 0.22222222. If it is not a pattern, like 0.568964329, it is an irrational number.
That isn't possible. Rational numbers either terminate or have a repeating pattern, and irrational numbers are all the rest. Perfect squares terminate, therefore they are rational.
Decimal numbers that never end but that end up having a repeating pattern are called recurring decimals or repeating decimals.Examples would be 1/3 = 0.33333333...or 452/555 = 0.8144144144144144... (where 144 is the repeating pattern).Reaching that repeating pattern is known as becoming periodic. Only rational numbers will have a repeating pattern. (The repeating pattern may be 00000, as in 4/2 = 2.00000... .)If a decimal number continues forever without having a repeating pattern, then it is a irrational number. One example of a number that continues forever without repeating would be π (pi) which continues infinitely without repeating.Pi is also referred to as a transcendental number.
Sometimes. Ellipses are used in repeating decimals like 7.4444... or 8.121212... to show that the pattern repeats forever. Repeating decimals are rational. Ellipses are also used in non-repeating, non-terminating decimals like pi = 3.14159... . Non-repeating, non-terminating decimals are irrational.
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).
.833 IS a repeating decimal. This is a rational number as well as it has a repetitive pattern.
The number 75.082106 with a repeating decimal is rational. A rational number can be expressed as a fraction of two integers, where the denominator is not zero. In this case, the repeating decimal can be written as a fraction, making it a rational number. Irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.