pi is an irrational number. It can not be expressed as a ratio of two integers.
Yes, the number 6.415418 repeating is a rational number because it can be expressed as a fraction of two integers. The repeating decimal indicates that the digits after the decimal point continue indefinitely in a predictable pattern, which is a characteristic of rational numbers. Therefore, it can be represented in the form of ( \frac{p}{q} ), where ( p ) and ( q ) are integers, and ( q ) is not zero.
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.
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.
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.
Yes, the number 6.415418 repeating is a rational number because it can be expressed as a fraction of two integers. The repeating decimal indicates that the digits after the decimal point continue indefinitely in a predictable pattern, which is a characteristic of rational numbers. Therefore, it can be represented in the form of ( \frac{p}{q} ), where ( p ) and ( q ) are integers, and ( q ) is not zero.
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).
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.
.833 IS a repeating decimal. This is a rational number as well as it has a repetitive pattern.