Visualise 4 . 26 ¯ on the number line, up to 4 decimal places.

We have, 4 . 26 ¯ = 4 . 2626 upto four decimal places 1 . ) To represent 4 . 2626 on number line divide the line segment between 4 and 5 into 10 equal parts representing 4 . 1 , 4 . 2 , . . . . . . 5 4 . 2626 lies between 4 . 2 & 4 . 3 . 2 . ) Magnify the segment between 4 . 2 & 4 . 3 and divide it into ten equal parts, representing 4 . 21 , 4 . 22 , 4 . 23 , . . . . . . 4 . 29 , 4 . 3 and 4 . 2626 lies between 4 . 26 & 4 . 27 3 . ) Magnify the segment between 4 . 26 & 4 . 27 and divide it into ten equal parts, representing 4 . 261 , 4 . 262 , . . . . . 4 . 27 and 4 . 2626 lies between 4 . 262 & 4 . 263 . 4 . ) Magnify the segment between 4 . 262 & 4 . 263 and divide it into ten equal parts, representing 4 . 2621 , 4 . 2622 , . . . . . 4 . 263 .

Simplify each of the following expressions: 3 + 3 2 + 2

Multiplying the terms, we get 3 + 3 2 + 2 = 3 2 + 3 2 + 3 2 + 3 2 = 6 + 3 2 + 2 3 + 6

Simplify the following expression: 5 + 2 2

Simplifying using, a + b 2 = a 2 + 2 a b + b 2 5 + 2 2 = 5 + 2 5 + 2 = 5 5 + 5 2 + 2 5 + 2 2 = 5 + 10 + 10 + 2 = 7 + 2 10

Recall, π is defined as the ratio of the circumference (say c ) of a circle to its diameter (say d ). That is, π = c d . This seems to contradict the fact that is irrational. How will you resolve this contradiction?

There is no contradiction at all. When we measure a length with scale or any other instrument, we only obtain an approximate rational value like 22 7 which is rational. We never obtain, the exact value. For this reason, we may not realize, that either c or d is irrational. Therefore, the fraction c d is irrational. Hence, π is irrational.

Represent 9 . 3 on the number line.

Mark the distance 9 . 3 units from a fixed point A on a given line to obtain a point B such that A B = 9 . 3 units. From B , mark a distance of 1 unit and the new point as C . Find the midpoint of A C and mark the point as O . Draw a semi-circle with centre O and radius O C . Draw a perpendicular to A C passing through B and intersecting the semi-circle at D . Then, B D = 9 . 3 To represent 9 . 3 on the number line. Consider the line B C as the number line, with B as 0 and C as 1 . Draw and arc with centre B and radius B D , which intersects the number line at E . Then E represents 9 . 3

E M B I B E

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONS

A K Upadhyay and S Upadhyay Solutions for Chapter: Number System, Exercise 4: NCERT EXERCISES WITH SOLUTIONs

Author:A K Upadhyay & S Upadhyay

A K Upadhyay Mathematics Solutions for Exercise - A K Upadhyay and S Upadhyay Solutions for Chapter: Number System, Exercise 4: NCERT EXERCISES WITH SOLUTIONs

Attempt the practice questions on Chapter 1: Number System, Exercise 4: NCERT EXERCISES WITH SOLUTIONs with hints and solutions to strengthen your understanding. MATHEMATICS solutions are prepared by Experienced Embibe Experts.

Questions from A K Upadhyay and S Upadhyay Solutions for Chapter: Number System, Exercise 4: NCERT EXERCISES WITH SOLUTIONs with Hints & Solutions

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONs>Q 1

Visualise $3.765$ on the number line, using successive magnification.

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONs>Q 2

Visualise $4 . \bar{26}$ on the number line, up to $4$ decimal places.

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONs>Q 2

Simplify each of the following expressions:

$(3 + \sqrt{3}) (2 + \sqrt{2})$

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONs>Q 2

Simplify the following expression:

$(3 + \sqrt{3}) (3 - \sqrt{3})$

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONs>Q 2

Simplify the following expression:

${(\sqrt{5} + \sqrt{2})}^{2}$

EASY

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONs>Q 2

Simplify the following expression:

$(\sqrt{5} - \sqrt{2}) (\sqrt{5} + \sqrt{2})$

MEDIUM

9th CBSE

IMPORTANT

MATHEMATICS>Chapter 1 - Number System>NCERT EXERCISES WITH SOLUTIONs>Q 3

Recall, $π$ is defined as the ratio of the circumference (say $c$ ) of a circle to its diameter (say $d$ ). That is, $π = \frac{c}{d}$ . This seems to contradict the fact that is irrational. How will you resolve this contradiction?