RD Sharma solutions for Mathematics for Class 9 chapter 1 - Number Systems [Latest edition]

Is zero a rational number? Can you write it in the form p/q, where p and q are integersand q ≠ 0?

Find five rational numbers between 1 and 2.

Find six rational numbers between 3 and 4.

Find five rational numbers between 3/5 and 4/5.

State whether the following statement is true or false. Give reasons for your answers.

Every whole number is a natural number.

State whether the following statement is true or false. Give reasons for your answers.

Every integer is a rational number.

State whether the following statement is true or false. Give reasons for your answers.

Every rational number is an integer.

State whether the following statement is true or false. Give reasons for your answers.

Every natural number is a whole number.

State whether the following statement is true or false. Give reasons for your answers.

Every integer is a whole number.

State whether the following statement is true or false. Give reasons for your answers.

Every rational number is a whole number.

Express the following rational number as decimal:

`42/100`

Express the following rational number as decimal:

`327/500`

Express the following rational number as decimal:

`15/4`

Express the following rational number as decimal:

`2/3`

Express the following rational number as decimal:

`-4/9`

Express the following rational number as decimal:

`-2/15`

Express the following rational number as decimal:

`-22/13`

Express the following rational number as decimal:

`437/999`

Express the following rational number as decimal:

`33/26`

Look at several examples of rational numbers in the form p/q (q≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Express the following decimal in the form `p/q` : 0.39

Express the following decimal in the form `p/q` : 0.750

Express the following decimal in the form `p/q` : 2.15

Express the following decimal in the form `p/q`:

7.010

Express the following decimal in the form `p/q`: 9.90

Express the following decimal in the form `p/q`: 1.0001

Express the following decimal in the form `p/q`: `0.bar4`

Express the following decimal in the form `p/q`: `0.bar37`

Express the following decimal in the form `p/q`: `0.bar54`

Express the following decimal in the form `p/q`: `0.bar621`

Express the following decimal in the form `p/q`: `125.bar3`

Express the following decimal in the form `p/q`: `4.bar7`

Express the following decimal in the form `p/q`: `0.4bar7`

Define an irrational number ?

Explain, how irrational numbers differ from rational numbers ?

Examine, whether the following number are rational or irrational:

`sqrt7`

Examine, whether the following number are rational or irrational:

`sqrt4`

Examine, whether the following number are rational or irrational:

`2+sqrt3`

Examine, whether the following number are rational or irrational:

`sqrt3+sqrt2`

Examine, whether the following number are rational or irrational:

`sqrt3+sqrt5`

Examine, whether the following number are rational or irrational:

`(sqrt2-2)^2`

Examine, whether the following number are rational or irrational:

`(2-sqrt2)(2+sqrt2)`

Examine, whether the following number are rational or irrational:

`(sqrt2+sqrt3)^2`

Examine, whether the following number are rational or irrational:

`sqrt5-2`

Classify the following number as rational or irrational :-

`sqrt23`

Classify the following number as rational or irrational :-

`sqrt225`

Classify the following number as rational or irrational :-

0.3796

Classify the following number as rational or irrational :-

7.478478...

Classify the following number as rational or irrational :-

1.1010010001...

Identify the following as rational or irrational number. Give the decimal representation of rational number:

`sqrt4`

Identify the following as rational or irrational number. Give the decimal representation of rational number:

`3sqrt18`

Identify the following as rational or irrational number. Give the decimal representation of rational number:

`sqrt1.44`

Identify the following as rational or irrational number. Give the decimal representation of rational number:

`sqrt(9/27)`

Identify the following as rational or irrational number. Give the decimal representation of rational number:

`-sqrt64`

Identify the following as rational or irrational number. Give the decimal representation of rational number:

`sqrt100`

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

x² = 5

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

y² = 9

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

z² = 0.04

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

`u^2=17/4`

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

v² = 3

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

w² = 27

In the following equation, find which variables x, y, z etc. represent rational or irrational number:

t² = 0.4

Give two rational numbers lying between 0.232332333233332... and 0.212112111211112.

Give two rational numbers lying between 0.515115111511115... and 0.535335333533335...

Find one irrational number between 0.2101 and 0.222... = `0.bar2`

Find a rational number and also an irrational number lying between the numbers 0.3030030003... and 0.3010010001...

Find three different irrational numbers between the rational numbers `5/7" and "9/11.`

Give an example of two irrational numbers whose:

difference is a rational number.

Give an example of two irrational numbers whose:

difference is an irrational number.

Give an example of two irrational numbers whose:

sum is a rational number.

Give an example of two irrational numbers whose:

sum is an irrational number.

Give an example of two irrational numbers whose:

product is an rational number.

Give an example of two irrational numbers whose:

product is an irrational number.

Give an example of two irrational numbers whose:

quotient is a rational number.

Give an example of two irrational numbers whose:

quotient is an irrational number.

Find two irrational numbers between 0.5 and 0.55.

Find two irrational numbers lying between 0.1 and 0.12.

Prove that `sqrt3+sqrt5` is an irrational number.

Complete the following sentence:

Every point on the number line corresponds to a _________ number which many be either _______ or ________.

Complete the following sentence:

The decimal form of an irrational number is neither ________ nor _________

Complete the following sentence:

The decimal representation of a rational number is either ______ or _________.

Complete the following sentence:

Every real number is either ______ number or _______ number.

Find whether the following statement is true or false.

Every real number is either rational or irrational.

Find whether the following statement is true or false.

π is an irrational number.

Find whether the following statement is true or false.

Irrational numbers cannot be represented by points on the number line.

Represent `sqrt6,` `sqrt7,` `sqrt8` on the number line.

Represent `sqrt3.5,` `sqrt9.4,` `sqrt10.5` on the real number line.

Visualise 2.665 on the number line, using successive magnification.

Visualise the representation of `5.3bar7` on the number line upto 5 decimal places, that is upto 5.37777.

Mark the correct alternative in the following:

Which one of the following is a correct statement?

Which one of the following statements is true?

Which of the following is a correct statement?

Which of the following statements is true?

Which of the following is irrational?

Which of the following is irrational?

Which of the following is rational?

The number 0.318564318564318564 ........ is:

If n is a natural number, then  \[\sqrt{n}\] is 

Which of the following numbers can be represented as non-terminating, repeating decimals?

Every point on a number line represents

Which of the following is irrational?

The number \[1 . \bar{{27}}\] in the form \[\frac{p}{q}\] , where p and q are integers and q ≠ 0, is

The number \[0 . \bar{3}\] in the form \[\frac{p}{q}\],where p and q are integers and q ≠ 0, is

\[0 . 3 \bar{2}\] when expressed in the form \[\frac{p}{q}\] (p, q are integers q ≠ 0), is

\[23 .  \bar{{43}}\] when expressed in the form \[\frac{p}{q}\] (p, q are integers q ≠ 0), is

\[0 . \bar{{001}}\] when expressed in the form \[\frac{p}{q}\]  (p, q are integers, q ≠ 0), is

`"The value of "0.overline23  0.overline22  "is" `

An irrational number between 2 and 2.5 is

The number of consecutive zeros in \[2^3    \times  3^4    \times  5^4    \times 7\] is

The smallest rational number by which`1/3`should be multiplied so that its decimal expansion terminates after one place of decimal, is

Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`