# Rational Numbers

## Trending Questions

**Q.**

Write a rational number between $\sqrt{2}$ and $\sqrt{3}$.

**Q.**prove that root 2 + root 5 is irrational

**Q.**

Find five rational numbers between $\frac{2}{3}$ and $\frac{4}{5}$.

**Q.**

Find five Rational numbers between $1$ and $2$.

**Q.**

Find five rational numbers between $\frac{1}{2}$ and $\frac{1}{3}$.

**Q.**

Is 2/root3 is rational or not.

**Q.**

Is zero a rational number? Can you write it in the form $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$ ?

**Q.**

Explain why 3.¯¯¯¯¯¯¯¯¯¯¯1416 is a rational number.

**Q.**Which of the following rational numbers is in the standard form?

- −928
- −2678
- −1416
- 4896

**Q.**

All surds are irrational but not all irrational numbers are surds. True/False.

False

True

**Q.**

Find five rational numbers between $\frac{1}{4}$ and $\frac{1}{2}$.

**Q.**

If pq is a rational number with terminating decimal expansion where p and q are coprimes, then q can be represented as:

(Here, n and m are non-negative integers.)

2 or 5 or both

3 or 5 or both

2 or 3 or both

2, 3 or 5

**Q.**

Division of rational number by a rational number.

**Q.**

The reciprocal of an irrational number is :

An integer

Rational

Irrational

None of these

**Q.**Given that HCF (306 and 657)=9, find LCM of (306 and 657)

**Q.**

In the standard form of a rational number, the denominator is always a

$0$

negative integer

positive integer

$1$

**Q.**

Insert4 irrational numbers between 3×root 2 and 2× root3

**Q.**

Decide whether the real number 0.120 1200 12000 120000.... is rational or not. If rational, and of the form pq, what can you say about the prime factors of q?

**Q.**

show that the reciprocal of 3+2 root 2 is an irrational number

**Q.**

Prove that 7 root 5 is irrational

**Q.**A rational number (of form p/q) has a terminating decimal expansion if prime factorisation of q has only:

- 3 or 4 or both
- 4 or 5 or both
- 6 or 7 or both
- 2 or 5 or both

**Q.**Find the LCM and HCF of the following pairs of integers and verify that LCM ×HCF = product of the two numbers.

(i) 336 and 54

**Q.**

Prove that √x + √y is irrational, where x and y are primes.

**Q.**

Decide whether the real number with decimal expansion as 125.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯987654321 is rational or not. If rational, and of the form pq, what can you say about the prime factors of q? :

Rational Number, Prime factors of q will be of form 2n.5m , m and n are whole numbers.

Not rational Number

Rational Number, prime factor cannot be represented in the form 2n.5m, m and n are whole numbers.

Rational Number, Prime factor of q will be 3.

**Q.**All of the following are rational numbers between 1 and 2 except 11/10. 193/100. 1714/1000. 903/1000

**Q.**

A number ‘s’ is called irrational if it cannot be written in the form of _____ , where p and q are integers and ______.

pq , q=0

pq , q≠0

pq , p≠0

pq , p=0

**Q.**Subtraction of a rational number and an irrational number gives

- a rational number
- an irrational number
- zero

**Q.**State whether the real number 52.0521 is rational or not. If it is rational express it in the form pq, where p, q are co - prime, integers and q≠0. What can you say about prime factorisation of q?

**Q.**Draw the graphs of the equations x−y+1=0 and 3x+2y−12=0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.

**Q.**The combined set of rational and irrational numbers forms the set of real numbers.

- True
- False