pi is an irrational number. It can not be expressed as a ratio of two integers.
No An irrational number goes on forever with no repeating pattern.
If the decimal is rational if it continues in a pattern. ex 2.586586586586586.... It is irrational if it continues forever without a pattern. ex 2.586943732434006843...
An irrational number by definition can not be exactly represented by a decimal that terminates or recurs. The moment a decimal terminates, or settles into a repeating pattern, it is rational.
either irrational numbers, integers, integers, rational numbers, or whole numbers
The number 3.456 repeating (often written as (3.456\overline{456})) is a rational number because it can be expressed as a fraction. Rational numbers are defined as numbers that can be written in the form ( \frac{a}{b} ), where ( a ) and ( b ) are integers and ( b \neq 0 ). Since 3.456 repeating has a repeating decimal pattern, it fits this definition.
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.
No An irrational number goes on forever with no repeating pattern.
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.
Written terminating as it does, it is a rational number. If that is the first bit with the 6 repeating forever (1.666...), then it is still a rational number. Irrational numbers as those numbers in decimal format that neither terminate nor end with a repeating sequence of digits.
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.
Correct -
If the decimal is rational if it continues in a pattern. ex 2.586586586586586.... It is irrational if it continues forever without a pattern. ex 2.586943732434006843...
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.
True
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.
A number with a finite number of decimal digits is always rational. (If the number of decimal digits is infinite, the number is rational only if there is a repeating pattern.)
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.