Tag: properties of irrational numbers

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Questions Related to properties of irrational numbers

Multiple choice maths number systems existence of irrational numbers irrational numbers properties of irrational numbers
The value of  $\displaystyle \pi $ upto $50$ decimal places is $:\:314159265358979323846264338327950288419716939937510$
Which are the least occurring digits?
  1. $0$
  2. $1$
  3. $2$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We will be considering the digits only after the decimal point.


Digit after decimal point frequency
0 2
1 5
2 5
3 8
4 4
5 5
6 4
7 4
8 5
9 8
Total 50

The maximum occurring digits are 3 and 9. 
The least occurring digit is 0.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which of the following is irrational?

  1. $\dfrac {22}{7}$
  2. $3.141592$
  3. $2.78181818$
  4. $0.123223222322223.......$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

An irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals.
Among all the options only $(D)$ $0.123223222322223$...... is non terminating and non repeating decimal.Therefore, it is a irrational number.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

$\sqrt 7$ is

  1. A rational number

  2. An irrational number

  3. Not a real number

  4. Terminating decimal
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rational numbers are those numbers which can be expressed in the form $ \dfrac {p}{q} $, where p and q are integers and $ q \neq 0 $
Numbers which are not rational numbers are called irrational numbers.
Since, $ \sqrt {7} $ cannot be written in $ \dfrac {p}{q} $, where $p$ and $q$ are integers and $ q \neq 0 $; it is an irrational number.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Classify the following numbers as rational or irrational : $2-\sqrt{5}$

  1. Irrational number

  2. Rational number

  3. Less Data

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$2$ is rational

$\sqrt 5 =2.035.........$ which is non terminating and non repeating hence irrational number.
We know that rational- irrational= irrational number.
Hence $2-\sqrt 5= irrational \,  number$
Hence, option A is the correct answer.

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Decimal representation of an irrational number is always

  1. Terminating

  2. Terminating, Repeating

  3. Non-Terminating, Repeating

  4. Non-Terminating, Non-Repeating
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Decimal representation of an irrational number is always non terminating non repeating.

 For example,$\sqrt{2}$ $=1.41421356237309504880168872420969807856967187537694807317667973799...$

Multiple choice maths rational and irrational numbers existence of irrational numbers irrational numbers properties of irrational numbers

Which among the following is true?

  1. There is no rational number between two irrational numbers.
  2. If ${x}^{2}=0.4$,then x is a rational number.

  3. The only real numbers are rational numbers.

  4. The reciprocal of an irrational number is irrational.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Option D is correct because the reciprocal of an irrational number (like 1/sqrt(2)) is also irrational. Option A is false as there are infinitely many rational numbers between any two irrational numbers. Option B is false because x = sqrt(0.4) is irrational. Option C is false because irrational numbers are also real numbers.