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Irrational Numbers

An irrational number is a number that can't be expressed by a fraction having integers in both its numerator and denominator. While their existence was once kept secret from the public for philosophical reasons, they are now well accepted, yet still surprisingly hard to prove on an individual basis. Please post all questions about irrational numbers, including the famous examples of π, e, and √2, into this category.

500 Questions

Is 188 rational irrational?

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Definitely RATIONAL.

Remember , casually irrational numbers are those decimals that go to inifinity , and the decimal digits are not in any regular order.

pi = 3.1415926.... is probably the most well known irrational number.

Other irrational numbers are the Sqyare roots of prime numbers.

e.g. sqrt(2) = 1.414213562....

sqrt(3) = 1.732508080....

sqrt(5) = 2.236067978....

More formally an Irrational number cannot be converted to a quotient (fraction).

Is negative three an irrational number?

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NO!!! It is an integer.

Casually irrational numbers are those where the decimal digits go to infinity and there is no regular order in the decimal number sequence.

pi = 3.1415926.... Is probably the most well known irrational number.

Is 0.77777 a irrational number?

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No because if need be it can be expressed as a fraction and so therefore it is a rational number

IS 8i an irrational number?

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No, it is an imaginary number.

Is the square root of 32 rational?

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sqrt(32) = 4sqrt(2)

The square root of '2' is irrational, so the square root of '32' is irrational.

Is 0.35 repeating a rational or irrational number?

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Rational, because it can be converted to a fraction .

Let

P = 0,353535....&

100P = 35.353535...

Subtract

99P = 35.0

P = 35/99 This will not reduce any further.

NB An IRRATIONAL number can be casually thought of as a decimal were the digits go to infinity , and there is no regular order in the digits.

pi = 3.141592... is probably the most well known irrational number.

Other irrational; numbers being the square root of prime numbers.

e.g.

sqrt(2) = 1.414213562....

Is pi divided by 2 rational or irrational?

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If a numerator and/or denominator in a fraction is irrational, the entire fraction is irrational. Since pi is irrational, pi divided by two is also irrational.

Is 7.76 irrational or rational?

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Rational , because it can be converted to a fraction.

7.76 = 7 76/100 = 7 38/50 = 7 19/25

NB Irrational numbers cannot be converted tpo a quotient.

'pi = 3.1415936.... ' it the most famous irrational number.

When you are given pi = 3.14' in school , this is only an approximation.

Is the square root of 0.09 rational?

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sqrt(0.09 is rational because you can convert it to a quotient.

sqrt(0.09) = 0.3 = 3/10 a quotient.

What number comes after 1100?

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The next integer is 1101, but there is no next number.

Is 2.3333..... irrational or rational?

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It is rational.

Any number that has a digit, or group of digits, that repeat forever is rational.

Is the number 0.1111 repeats is it irrational?

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NO!!!!

It can be converted to a rational fraction.

Method.

Let P 0.6666....

& 10P = 6.6666....

Subtract

9P = 6.0 = 6

P = 6/9

P = 2/3

With Irrational numbers you cannot convert to a fraction.

Casually an irrational number is one which goes to infinity, but the digits are not in any regular order. pi = 3.141592654.. is probably the most famous irrational number. Others being the square root (2) = 1.414213562....

and the square roots of prime numbers.

How do you write 9.98 million in numbers?

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9.98 million = 9,980,000

In word it is said as 'Nine million, nine hundred and eighty thousand'.

Is 1.35 irrational or rational?

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1.35 is a rational number that can also be expressed as a fraction.

Is the decimal form of an irrational number a repeating decimal?

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An irrational number must not have a repeating sequence. If we have a number, such as 0.333333...., we can turn this into a rational number as such.

Let x = 0.333333......, then multiply both sides by 10:

10x = 3.333333......

Now subtract the first equation from the second, since the 3's go on forever, they will cancel each other out and you're left with:

9x = 3. Now divide both sides by 9: x = 3/9 which is 1/3, a rational number equal to 0.3333333....

If a number can be expressed as the ratio a/b, where a and b are integers (with the restriction that b not equal zero), then the number is rational. If you cannot express the number as such, then it is irrational.

Why irrational numbers are roots?

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Irrational numbers can be roots because they are solutions to certain mathematical equations. For example, the square root of 2 is an irrational number that is a solution to the equation x^2 = 2. Similarly, other irrational numbers can be roots of different equations depending on their mathematical properties.

What is the square root of 25 and 75 simplified?

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The square root of 25 simplifies to 5, and the square root of 75 does not have a simplified whole number value.

Is the square root of 432.8 rational?

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No, the square root of 432.8 is an irrational number because it cannot be expressed as a fraction of two integers.

Examples of set of real numbers?

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Some examples of sets of real numbers include:

  1. The set of positive integers: {1, 2, 3, 4, ...}
  2. The set of rational numbers: {1/2, -3/4, 5/6, ...}
  3. The set of whole numbers: {..., -2, -1, 0, 1, 2, ...}
  4. The set of natural numbers: {0, 1, 2, 3, 4, ...}
  5. The set of irrational numbers: {√2, π, e, ...}

Is the square of a number irrational Always sometimes never?

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The square of a rational number can be either rational or irrational. However, the square of an irrational number is always irrational.

Is 0.000125 an irrational number?

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NO!!!!

An irrational number is one were the decimal digits go to infinity and are not in any regular ordert.

Since 0.000125 terminates at the sixth decimal digit it does not go to infinity. Also irrational numbers cannot be converted to fractions. 0.000125 can be converted to a fraction.

Hence

0.000125 / 1.000000

Cancel down the decimal point, and the prefix zeroes.

Hence

125/1000000

Cancel down by '5'

25/200000

Cancel down again by '5'

5/ 40000

Cancel down by '5' again !!!!

1/8000

The answer!!!!!

NB

pi = 3.141592.... is the most well known irrational number.

Also the square roots of prime numbers e.g.

sqrt(2) = 1.414213562....

Is 5 over pi a rational or irrational number?

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If you divide a rational number by an irrational number, or vice versa, you will ALMOST ALWAYS get an irrational result. The sole exception is if you divide zero (which is rational) by any irrational number.