3.142678 = 3142678/1000000 , It is of the form ?/? , where p = 3142678, q = 1000000 hence is a rational number.
Hence, 3.142678 is a rational number and it can be expressed as \[\dfrac{{3142678}}{{1000000}}\] in $\dfrac{p}{q}$ form. Note: Here, we can also express the obtained fraction in simplest form.
Here is your answer - it is terminating.
Students are usually introduced to the number pi as having an approximate value of 3.14 or 3.14159. Though it is an irrational number, some people use rational expressions, such as 22/7 or 333/106, to estimate pi.
Answer: If a number can be written or can be converted to p/q form, where p and q are integers and q is a non-zero number, then it is said to be rational and if it cannot be written in this form, then it is irrational.
Rational numbers include fractions and any number that can be expressed as fractions. Natural numbers, whole numbers, integers, fractions of integers, and terminating decimals are rational numbers. Non-terminating decimals with repeating patterns of decimals, that is recurring decimals are also rational numbers.
(i) All whole numbers are rational numbers. (ii) Negative integers are not rational numbers.
c 3.142857 is rational because it is a terminating decimal.
D) 3.141141114 is an irrational number because it has not terminating non repeating decimal expansion.
Because 3.141141114... is neither a repeating decimal nor a terminating decimal, it is an irrational number.
pi is an irrational number. Since it is a non-repeating, non-terminating decimal, it cannot be written as a fraction. The symbol for pi is "π". π = 3.141 592 653 589 793 238 462 643 383 279 ...
Rational Numbers as Terminating and Non-Terminating Decimals
Terminating decimals are numbers that end after a few repetitions, after the decimal point. Example: 0.6, 4.789, 274.234 are some examples of terminating decimals. Non-terminating decimals are numbers that keep going after the decimal point.
Every terminating decimal is a rational number but every rational number may not be a terminating decimal.
Jeremy says that 5.676677666777... is a rational number because it is a decimal that goes on forever with a pattern. Is he correct? Why or why not? Yes, because the decimal is repeating.
Justification: Since 1.010010001 is non - terminating non - recurring decimal number, therefore it cannot be written in the form p/q; q≠0, p, q both are integers. Thus, 1.010010001 is irrational.
π is an irrational number. Hence, it is a real number.
Hence, 0.666666.. is a rational number.
Apart from this the given decimal number has recurring number 1416, hence it is a rational number. Q. Explain why.
3.141141114 is an irrational number because it is a non-repeating and non-terminating decimal.
Pi, 3.14159265359, is an irrational number. That means it can't be expressed as a simple fraction.
The number 0.14114111411114 . . . is irrational because it may not be expressed as the ratio of two integers. It is not a repeating decimal.
3.333333........ is a recurring non terminating decimal. repeating, it is a rational number.
The common examples of irrational numbers are pi(π=3⋅14159265…), √2, √3, √5, Euler's number (e = 2⋅718281…..), 2.010010001….,etc.
Specifically, the Greeks discovered that the diagonal of a square whose sides are 1 unit long has a diagonal whose length cannot be rational. By the Pythagorean Theorem, the length of the diagonal equals the square root of 2. So the square root of 2 is irrational!