NCERT Solutions for Class 9 Maths Chapter 1 Number Systems

Category: CBSE, Class 9

Post Published On:

4 min read

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Excercise 1.1
Question 1. Is zero a rational number? Can you write it in the form `\frac{p}{q}`,where p and q are integers and q ≠0?
Solution: Yes, zero is a rational number it can be written in the form `\frac{p}{q}`.
0 = `\frac{0}{1}=\frac{0}{2}=\frac{0}{3}` etc. denominator q can also be taken as negative integer.
Question 2. Find six rational numbers between 3 and 4.
Solution: Let qi be the rational number between 3
and 4, where j = 1 to 6.
∴ Six rational numbers are as follows:
q1=`\frac{3+4}{2}=\frac{7}{2};3<\frac{7}{2}<4`
q2=`\frac{3+ \frac{7}{2} }{2}= \frac{ \frac{13}{2}}{2}= \frac{13}{4};3< \frac{13}{4}< \frac{7}{2}<4`
q3=`\frac{4+ \frac{7}{2} }{2}= \frac{ \frac{15}{2}}{2}= \frac{15}{4};3< \frac{13}{4}< \frac{7}{2}< \frac{15}{4} <4`
q4=`\frac{ \frac{7}{2}+ \frac{13}{4} }{2}= \frac{ \frac{14+13}{4}}{2}= \frac{ \frac{27}{4}}{2}= \frac{27}{8};3< \frac{13}{4} < \frac{27}{8}< \frac{7}{2}< \frac{15}{4}<4`
q5= `\frac{1}{2}(\frac{7}{2}+ \frac{15}{4}) = \frac{1}{2} ( \frac{14+15}{4} )=\frac{29}{8};3< \frac{13}{4} < \frac{27}{8}< \frac{7}{2} < \frac{29}{8}< \frac{15}{4}<4`
q6= `\frac{1}{2}(\frac{13}{4}+ \frac{27}{8}) = \frac{1}{2} ( \frac{26+27}{8} )=\frac{53}{16};3< \frac{13}{4} < \frac{53}{16} < \frac{27}{8} <\frac{7}{2}< \frac{29}{8}< \frac{15}{4}<4`
Thus, the six rational numbers between 3 and 4 are
`\frac{7}{2},\frac{13}{4},\frac{15}{4},\frac{27}{8},\frac{29}{8}and\frac{53}{16}`
Question 3.Find five rational numbers between `\frac{3}{5}` and `\frac{4}{5}`.
Solution:Since, we need to find five rational numbers, therefore, multiply numerator and denominator by 6.
∴ `\frac{3}{5}= \frac{3×6}{5×6}= \frac{18}{30}and \frac{4}{5}= \frac{4×6}{5×6}= \frac{24}{30}`
∴ Five rational numbers between `\frac{3}{5}and\frac{4}{5}are\frac{19}{30},\frac{20}{30},\frac{21}{30},\frac{22}{30},\frac{23}{30}`
Question 4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
(ii) Every integer is a whole number.
(iii) Every rational number is a whole number.
Solution:(i) True
∵ The collection of all natural numbers and 0 is called whole numbers.
(ii) False
∵ Negative integers are not whole numbers.
(iii) False
∵ Rational numbers are of the form `\frac{p}{q}`, q ≠ 0 and q does not divide p completely that are not whole numbers.

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

Question 1. 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 √m , where m is a natural number.
(iii) Every real number is an irrational number.
Solution:(i) True
Because all rational numbers and all irrational numbers form the group (collection) of real numbers.
(ii) False
Because negative numbers cannot be the square root of any natural number.
(iii) False
Because rational numbers are also a part of real numbers.
Question 2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
Solution: No, if we take a positive integer, say 9, its square root is 3, which is a rational number.
Question 3. Show how √5 can be represented on the number line.
Solution: Draw a number line and take point O and A on it such that OA = 1 unit. Draw BA ⊥ OA as BA = 1 unit. Join OB = √2 units.
Now draw BB1 ⊥ OB such that BB1 =1 unit. Join OB1 = √3 units.
Next, draw B1B2⊥ OB1such that B1B2 = 1 unit.
Join OB2 = units.
Again draw B2B3 ⊥OB2 such that B2B3 = 1 unit.
Join OB3 = √5 units.
Take O as centre and OB3 as radius, draw an arc which cuts the number line at D.
Point D
represents √5 on the number line.

Question 4. Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1, of unit lengths Draw a line segment P1, P2 perpendicular to OP1 of unit length (see figure). Now, draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn-1 Pn by drawing a line segment of unit length perpendicular to OPn – 1. In this manner, you will have created the points P2, P3,…… Pn,….. and joined them to create a beautiful spiral depicting √2,√3,√4,……

NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3

Question 1. Write the following in decimal form and say what kind of decimal expansion each has
`(i) \frac{36}{100} (ii) \frac{1}{11} (iii) 4\frac{1}{8} (iv) \frac{3}{13} (v) \frac{2}{11} (vi) \frac{329}{400}`
Solution:(i) We have, `\frac{36}{100}` = 0.36
Thus, the decimal expansion of `\frac{36}{100}` is terminating.
`\begin{array}{r}
\frac{536}{23) 12345} \\
\frac{115}{84} \\
\frac{69}{155} \\
\frac{138}{17}
\end{array}`
#\hspace{11.5mm}536#
#23\overline{)12345}#
#\hspace{7mm}\underline{115}#
#\hspace{11.5mm}84#
#\hspace{11.5mm}\underline{69}#
#\hspace{11.5mm}155#
#\hspace{11.5mm}\underline{138}#
#\hspace{14mm}17#
$\hspace{11.5mm}536$
$23\overline{)12345}$
$\hspace{7mm}\underline{115}$
$\hspace{11.5mm}84$
$\hspace{11.5mm}\underline{69}$
$\hspace{11.5mm}155$
$\hspace{11.5mm}\underline{138}$
$\hspace{14mm}17$
 
##\hspace{11.5mm}536##
##23\overline{)12345}##
##\hspace{7mm}\underline{115}##
##\hspace{11.5mm}84##
##\hspace{11.5mm}\underline{69}##
##\hspace{11.5mm}155##
##\hspace{11.5mm}\underline{138}##
##\hspace{14mm}17##

zusammenhängende Posts

Google Pixel 9: Nachrichten und erwarteter Preis, Veröffentlichungsdatum, Spezifikationen; und weitere Gerüchte

Samsung bringt 2 neue USB-Flash-Laufwerke mit je 512 GB auf den Markt.

Mit dem neuen Apple-Reparaturprogramm können einige gebrauchte Teile verbessert werden

Stichworte

Kommentare

Über uns

Anuragcareer

Anuragcareer hat nur ein Ziel: über alles zu berichten, was mit Technologie in unserem Leben zu tun hat.

Wir teilen nützliche, informative und unterhaltsame Informationen für Sie alle auf Deutsch.

Beliebte Beiträge

Google Pixel 9: Nachrichten und erwarteter Preis, Veröffentlichungsdatum, Spezifikationen; und weitere Gerüchte

Samsung bringt 2 neue USB-Flash-Laufwerke mit je 512 GB auf den Markt.

Mit dem neuen Apple-Reparaturprogramm können einige gebrauchte Teile verbessert werden

Die neue Pressemaschine von Apple löst ein Problem ohne Probleme.

Wichtige Seiten

Über uns

Kontaktiere uns

DMCA

Privacy Policy

Terms & Conditions

Phone: +17864540015
Email: contact@www.anuragcareer.com

Don`t copy text!