Rational Numbers

Q.

Why $\pi$ is irrational and $\frac{22}{7}$ is rational?

Q.

Is pi a rational or irrational number?

Q.

Every rational number is an integer. Why or why not? Give example

Q.

Every rational number is a whole number? True or false, also give reason of your answer.

1. True
2. False

Q.

Express $\frac{-42}{98}$ as a rational number with denominator 7.

Q.

Express each of the following rational numbers in standard form :

(i) $\frac{-12}{30}$ (ii) $\frac{-14}{49}$ (iii) $\frac{24}{-64}$ (iv) $\frac{-36}{-63}$

Q.

Which of the two rational numbers is greater in the given pair ?

(i) $\frac{3}{8}$ or 0 (ii) $\frac{-2}{9}$ or 0 (iii) $\frac{-3}{4}$ or $\frac{1}{4}$

(iv) $\frac{-5}{7}$ or $\frac{-4}{7}$ (v) $\frac{2}{3}$ or $\frac{3}{4}$ (vi) $\frac{-1}{2}$ or -1

Q. Question 142
Shaline has to cut out circles of diameter $1\frac{1}{4}cm$ from an aluminium strip of dimensions $8\frac{3}{4}cm$ by $1\frac{1}{4}cm$. How many full circles can Shalini cut? Also, calculate the wastage of the aluminium strip.

Q.

Express $\frac{-3}{5}$ as a rational number with denominator ?

(i) 20 (ii) -30 (iii) 35 (iv) -40

Q.

Sum of a rational and an irrational number is a/an

1. rational number

2. irrational number

3. real number

4. We can't add a rational and an irrational number

Q.

Express $\frac{-48}{60}$ as a rational number with denominator $5$.

Q. Question 96
Every whole number is a rational number

Q. Question 148
Roller coaster at an amusement park is $\frac{2}{3}$ m high. If a new roller coaster is built that is $\frac{3}{5}$ times the height of the existing coaster, what will be the height of the new roller coaster?

Q.

Which of the following statements are true?

(i) Every natural number is a rational number.

(ii) Every integer is a rational number.

(iii) 0 is a whole number but it is not a rational number.

1. (i), (ii) and (iii)

2. (i) and (ii)

3. (ii) and (iii)

4. (i)

Q.

Who discovered rational numbers? What are it's applications in our daily lives?

Q. Which rational number has no reciprocal?

1. 1
2. -1
3. 0
4. None of the above

Q.

All integers are rational numbers. Justify the statement

Q. Question 147
The overall width in cm of several wide-screen televisions are 97.28 cm, $98\frac{4}{9}cm,98\frac{1}{25}cm$ and 97.94 cm. Express these numbers as rational numbers in the form $\frac{p}{q}$ and arrange the widths in ascending order.

Q.

Ten hundred thousand $=$________ million

Q.

The table shows the portion of some common materials that are recycled.

Arrange the rate of recycling the materials from the greatest to the smallest.

Material	Recycled
Paper	$\frac{5}{11}$
Aluminium cans	$\frac{5}{8}$
Glass	$\frac{2}{5}$
Scrap	$\frac{3}{4}$

Q.

Why is zero called the identity for the addition of rational numbers

Q. Question 45
The rational number 10.11 in the form $\frac{p}{q}$ is ___

Q.

Question 151
A skirt that is $35\frac{7}{8}$ cm long has a hem of $3\frac{1}{8}$ cm. How long will the skirt be if the hem is let down?

Q. Question 93
If x and y are two rational numbers such that x > y, then x - y is always a positive rational number.

Q. Question 97
0 is whole number but it is not a rational number

Q. A number which can be expressed as $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is known as a/an

1. natural number
2. whole number
3. rational number
4. integer

Q.

Fill in the blanks :
(i) The product of two positive rational numbers is always___
(ii) The product of two negative rational numbers is always___
(iii) If two rational numbers have opposite signs then their product is always___
(iv) The reciprocal of a positive rational number is ___ and the reciprocal of a negative rational number is___
(v) Rational number 0 has___ reciprocal.
(vi) The product of a rational number and its reciprocal is ___
(vii) The numbers ___and ___are their own reciprocals.
(viii) If M is reciprocal on N, then the reciprocal of N is___

Q.

Express each of the following as a rational number in the form $\frac{p}{q}:$

$\left(i\right)6^{-1}\left(ii\right)(-7{)}^{-1}(iii\left){\left(\frac{1}{4}\right)}^{-1}\right(iv\left)\right(-4{)}^{-1}\times {\left(\frac{-3}{2}\right)}^{-1}\left(v\right){\left(\frac{3}{5}\right)}^{-1}\times {\left(\frac{5}{2}\right)}^{-1}$

Q. Express $\frac{-42}{98}$ as a rational number with denominator 7.

Q. Why is 0 considered as an even number?