Rational Numbers

Q.

Represent √7 on number line.

Q.

Express 0.99999…. in the form p/q . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Q.

Find three rational numbers lying between $\frac{3}{5}$ and $\frac{7}{8}$ .

How many rational numbers can be determined between these two numbers?

Q.

Insert 16 rational numbers between 2.1 and 2.2.

Q. An irrational number lying between $\frac{1}{7}$ and $\frac{2}{7}$ is

1. 0.29364859....
2. 0.72386....
3. 0.1456784.....
4. 0.141414...

Q.

Find four rational numbers between $\frac{3}{7}$ and $\frac{5}{7}$.

Q.

Write three rational numbers between $\sqrt{3}$ and $\sqrt{5}$.

Q.

Two rational numbers between $\frac{2}{3}$ and $\frac{5}{3}$ are

(a)$\frac{1}{6}$ and $\frac{2}{6}$
(b)$\frac{1}{2}$ and $\frac{2}{1}$
(c)$\frac{5}{6}$ and $\frac{7}{6}$
(d)$\frac{2}{3}$ and $\frac{4}{3}$

Q.

Insert three rational numbers between 3\5 and 2\3.

Q.

A number ${}^{\prime }{x}^{\prime }$was found to be represented in the simplest $\frac{p}{q}$ form. The decimal expansion of this number was found to be 5.3333333333..... Find the value of p - q.

1. 12

2. 13

3. 11

4. 14

Q.

Find $10$ rational numbers between $\frac{-3}{11}$ and $\frac{8}{11}$.

Q.

Write the number $0.\overline{35}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is

1. 

2. 

3. 

4. 

Q.

The product of two rational numbers is always a ______ number

Q. $(2+\sqrt{5})$ is a/an

1. Whole number
2. Natural number
3. Rational number
4. Irrational number

Q.

Find two rational numbers of the form $\frac{p}{q}$ between the numbers 0.2121121112....and 0.2020020002....

Q.

Find 24 rational numbers between 0 and 0.1

Q.

Find a rational number between -2 and 6

Q.

There are ______ rational numbers between any two rational numbers

Q.

Find two rational number between -2 and 5

Q.

Express the following rational numbers as decimals:

(i) $\frac{42}{100}$ (ii) $\frac{327}{500}$ (iii) $\frac{15}{4}$

Q.

Find five rational numbers between $0$ and $1$.

Q.

Insert three rational numbers between:

(i) $\frac{2}{5}$ and $\frac{3}{7}$

(ii) $\frac{4}{11}$ and $\frac{9}{16}$

Q.

State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.

(ii) Every point on the number line is of the form $\sqrt{m},$ where ${}^{\prime }{m}^{\prime }$ is a natural number.

(iii) Every real number is an irrational number.

Q.

In the following equations, find which variables x, y, z etc, represent rational or irrational numbers :

(i) $x^2$ = 5 (ii) $y^2$= 9

(iii) $z^2$ = 0.04 (iv) $u^2=\frac{17}{4}$

(v) $v^2$ = 3 (vi) $w^2$= 27

(vii) $t^2=0.4$

Q.

Features of high level language -

Q. Which one of the following statements is true?
(a) The sum of two irrational numbers is always an irrational number
(b) The sum of two irrational numbers is always a rational number
(c) The sum of two irrational numbers may be a rational number or an irrational number
(d) The sum of two irrational numbers is always an integer

Q. Represent root 19 on the number line by Pythagorean triplet.

Q.

Find 4 rational number between 1/5 and 1/6

Q.

A rational number equivalent to $\frac{7}{19}$ is

(a)$\frac{17}{119}$

(b)$\frac{14}{57}$

(c)$\frac{21}{38}$

(d)$\frac{21}{57}$

Q.

What is the absolute value of $\frac{0}{2}$?