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What type of numbers are said to be in rational form and are referred to as rational numbers?
Wiki User
∙ 6y ago
They are numbers which are written in the form p/q where p and q are integers.
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoFractions
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Is 18 rational or irrational?
irrational
What is a rational exponent in math?
If the exponent or raised power of a number is in the form of p/q the exponent is said to be rational exponent. For example= 11/2 22/3
All rational numbers are integers?
A rational number is a number which can be expressed as the quotient of two integers, a quotient being the solution to a division sum. Therefore, 1/2, or one half, is a rational number, equal to 0.5. However, 1/3, or one third, is an irrational number, because if you had to write the number out as a decimal, the number would continue to recur. Therefore, all integers are rational numbers, but not all rational numbers are integers. EDIT: 1/3 is a rational number, whoever said it wasn't is a moron.
Are there more rational than irrational numbers?
The answer requires a bit of mathematics, but goes like this:The product of any 2 rational numbers is a rational number.The product of any 2 irrational number is an irrational number.The product of a rational and an irrational number is an irrational number!Therefore simple logic tells us that there are more irrational numbers than rational numbers. There is a way to structure this mathematically, and I believe it is called an "Inductive Proof".Interesting !I'm going to say "No".I reason thusly:-- For every rational number 'N', you can multiply or divide it by 'e', add it to 'e',or subtract it from 'e', and the result is irrational.-- You can multiply or divide it by (pi), add it to (pi), or subtract it from (pi),and the result is irrational.-- You can take its square root, and more times than not, its square root is irrational.There may be others that didn't occur to me just now. But even if there aren't,here are a bunch of irrational numbers that you can make from every rational one.This leads me to believe that there are more irrational numbers than rational ones.-------------------------------------------------------------------------------------------------------There are infinitely many more irrationals than rationals; this was proved by G. Cantor (born 1845, died 1918). His proof is basically:The rational numbers can be listed by assigning to each of the counting numbers (1, 2, 3,...) one of the rational numbers in such a way that every rational number is assigned to at least one counting number;If it is assumed that every irrational number can be assigned to at least one counting numbers (like the rationals), then with such a list it is possible to find an irrational number that is not on the list; so is it not possible as there are more irrationals than there are counting numbers, which has shown to be the same size as the rational numbers, thus showing that there are more irrationals than rationals.
Can the product of a whole number and an irrational number be a rational number?
Most children learn about Pi and square roots somewhere during the middle school. They may hear said 'irrational number' and some even remember the phrase, but very few really understand what it means. Well, irrational numbers are harder to understand than rational numbers, but I consider it worth the time and effort because they have some fascinating properties. I just have to wonder in awe when I see the facts laid in front of me because it all sounds unbelievable, yet proven true.To study irrational numbers one has to first understand what are rational numbers. In short they are whole numbers, fractions, and decimals - the numbers we use in our daily lives.
Is There fewer rational numbers than irrational numbers.?
Yes. The infinity of rational numbers has the same size as the natural numbers, said to be "countable". The infinity of real numbers (and therefore, also of irrational numbers) is a larger infinity, said to be "uncountable".
A rational expression that cannot be simplified?
If there is no common factor other than 1 in a rational expression, it is in simplest terms or form.
What is the standard form of a rational number?
A rational number is said to be in the standard form if its denominator is a positive integer and the numerator and the denominator have no common factor other than 1 .If a rational number is not in the standard form , then it can be reduced to the standard form .
Is 18 rational or irrational?
irrational
What is the difference between decimal and rational number?
A number x is said to be rational if it can be expressed as the ratio p/q where p and q are integers, and q is not 0. For each rational number there is an equivalent decimal representation which is either a terminating decimal or one that has an infinitely recurring pattern. A decimal number which is infinite but without any recurring pattern is an irrational number.Thus rational numbers form a subset of decimal numbers.
Can a fraction be rational?
Yes it can. In fact, all real fractions are rational. Numbers are said to be rational that are ratios of the whole numbers. For example: 3/3 = 1 , therefore 1 is rational (and all other whole numbers) 2/3 = .666... , therefore .666... is rational because it is a ratio of 2 to 3. 123512/321235 also rational. There are some types of numbers, trancendental numbers, for example, for which no ratio exists. We call those numbers irrational. Famously, the number pi is the ratio between the diameter and circumfrence of a circle. There is no whole number ratio that can represent this relationship. Pi is both transendental and irrational.
What is a rational exponent in math?
If the exponent or raised power of a number is in the form of p/q the exponent is said to be rational exponent. For example= 11/2 22/3
All rational numbers are integers?
A rational number is a number which can be expressed as the quotient of two integers, a quotient being the solution to a division sum. Therefore, 1/2, or one half, is a rational number, equal to 0.5. However, 1/3, or one third, is an irrational number, because if you had to write the number out as a decimal, the number would continue to recur. Therefore, all integers are rational numbers, but not all rational numbers are integers. EDIT: 1/3 is a rational number, whoever said it wasn't is a moron.
What is the difference between rational numbers and whole numbers?
A whole number is usually defined as any non-negative integer (0, 1, 2, 3, ....). However, some limit the definition to all positive integers (1, 2, 3, ...), and others de-limit it to include all integers, whether positive, negative, or zero (... -2, -1, 0, 1, 2, ...). A rational number is any number that can be expressed as a ratio of two integers. Obviously, all integers are rational numbers because an integer can be expressed as a ratio of itself and 1 (i.e., 7 = 7/1). Also, all fractions in which both the enumerator and denominator are integers are rational numbers (that follows from the definition). But also, any decimal number that has a finite number of decimal places can be expressed as a ratio (4.5632674 = 45632674/10000000). Furthermore, any decimal number with an infinite number of decimal places, as long as they repeat, can be expressed as a ratio (0.333333... = 1/3). Basically, the only numbers that are not a rational numbers are those numbers for which both 1) there are an infinite number of decimal places, and 2) the digits in the decimal places never repeat themselves. Note that, when it is said that the decimal places "repeat", it need not be a single digit repeated infinitely. It could be a series of digits repeated infinitely. For example, 1/7 = 0.142857142857142857142857..., with the series "142857" repeated infinitely. Note also that, though not included in the examples above, negative numbers can be rational numbers (-7, -1/3, -4.5632674, and -0.142857142857142857142857... are all rational). In fact, any positive rational number can be made negative (and still remain rational), by multiplying it by -1. A number that is not rational is referred to as an "irrational number". Commonly seen examples include pi (3.14159262...), e (2.71828182845), and the square root of 2. Both rational and irrational numbers are part of the set of numbers referred to as "real numbers". This set encompasses all numbers that actually exist, from negative infinity to positive infinity, and every point in between.
Is 4.7010010001 a rational or irrational number and why?
It is rational. You can write its decimal part as 7,010,010,001/10,000,000,000. Add 40,000,000,000/10,000,000,000 to that and you get 47,010,010,001/10,000,000,000, a very ugly fraction that doesn't reduce. But hey, nobody ever said rational numbers were always going to look nice. It still equals 4.7010010001.
Are there more rational than irrational numbers?
The answer requires a bit of mathematics, but goes like this:The product of any 2 rational numbers is a rational number.The product of any 2 irrational number is an irrational number.The product of a rational and an irrational number is an irrational number!Therefore simple logic tells us that there are more irrational numbers than rational numbers. There is a way to structure this mathematically, and I believe it is called an "Inductive Proof".Interesting !I'm going to say "No".I reason thusly:-- For every rational number 'N', you can multiply or divide it by 'e', add it to 'e',or subtract it from 'e', and the result is irrational.-- You can multiply or divide it by (pi), add it to (pi), or subtract it from (pi),and the result is irrational.-- You can take its square root, and more times than not, its square root is irrational.There may be others that didn't occur to me just now. But even if there aren't,here are a bunch of irrational numbers that you can make from every rational one.This leads me to believe that there are more irrational numbers than rational ones.-------------------------------------------------------------------------------------------------------There are infinitely many more irrationals than rationals; this was proved by G. Cantor (born 1845, died 1918). His proof is basically:The rational numbers can be listed by assigning to each of the counting numbers (1, 2, 3,...) one of the rational numbers in such a way that every rational number is assigned to at least one counting number;If it is assumed that every irrational number can be assigned to at least one counting numbers (like the rationals), then with such a list it is possible to find an irrational number that is not on the list; so is it not possible as there are more irrationals than there are counting numbers, which has shown to be the same size as the rational numbers, thus showing that there are more irrationals than rationals.
Is 5.4 an irrational or rational number?
5.4 = 5 2/5 = 27/5 so it is a rational number.
