An irrational number is a real number that cannot be expressed as a ratio of integers; for example, √2 is an irrational number.
A recurring decimal is a number in which one or more digits at the end of a number after the decimal point repeats endlessly ( For example, 0.333….., 0.111111…, 0.166666…., etc. are all recurring decimals). Any recurring decimal can be expressed as a fraction of the form p/q and hence it is a rational number.
0.33333...... is it a rational number how? Dear Student, Any decimal number with repeating decimal is a rational number. 0.3333... is a rational number.
Is 3.14 a rational number? Yes, 3.14 is a rational number because it is terminating.
The number 25 is a rational number. It is a whole number that can be written as the fraction 25/1. By definition, a rational number is the number that results when one integer is divided by another integer. Since both 25 and 1 are integers, 25/1 represents an integer being divided by another integer.
D) 3.141141114 is an irrational number because it has not terminating non repeating decimal expansion.
c 3.142857 is rational because it is a terminating decimal.
Expert-Verified Answer. 3.14114114...... is an irrational number. Option (d) is correct.
(d) 0.4014001400014... is a non-terminating and non-recurring decimal and therefore is an irrational number.
Here in 3.33333............ , 3 gets repeated endlessly i.e. till infinity and hence is a rational number. This is seen to be a rational number pq , so it is not irrational.
Many non-integer, or decimal numbers, are also rational numbers. For instance, 8.75 can be rewritten as 8 3/4, 875/100, or 1750/200. This also includes repeating decimal numbers like 0.3333333..., which can be rewritten as 1/3.
The rational numbers are those which have repeating decimal expansions (for example 1/11=0.09090909..., and 1=1.000000... =0.999999...). They are also those which have terminating continued fraction expansions.
A number is rational if it is a terminating or a recurring decimal, such as \(\frac{1}{2}\) = 0.5, 0.99999… and so on. Irrational numbers, such as 0.31545673, are non-terminating and non-repeating decimals.
Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern.
However, we can see that there is no repeating pattern in the digits after the decimal point. Therefore, we can conclude that 0.8387667688386759__ is an irrational number because it has an infinite non-repeating decimal representation.
Ans: The number 0.101100101010 is a terminating decimal number, and the terminating decimals are considered as rational numbers, so this number is not an irrational number.
The number 0.14114111411114 . . . is irrational because it may not be expressed as the ratio of two integers. It is not a repeating decimal.
Hence, 0.666666.. is a rational number. Q. Which of the following is a rational number ? Q.
For example, take the number 0.33333... Even though this is often simplified as 0.33, the pattern of 3's after the decimal point repeat infinitely. This means that the number can be converted into the fraction 1/3, and is a rational number.
3.141141114 is an irrational number because it is a non-repeating and non-terminating decimal.
0.3796 is a rational number because it is a terminating decimal number.
The number 10 is a rational number. We know this because it is a whole number, or integer. All integers are rational numbers. Rational numbers are those which can be expressed as a ratio or fraction between two integers.
The square root of 41 is irrational.
The approximate value of the square root of 41 is 6.4. When 6.4 is multiplied by 6.4, the product is 40.96, which is approximately equal to 41. Since 6.4 is multiplied by itself, 6.4 is the nearest square root of 41.