Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 2.1- Real Numbers

Class 9: Maths Chapter 2.1 solutions. Complete Class 9 Maths Chapter 2.1 Notes.

Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 2.1- Real Numbers

Maharashtra Board 9th Maths Chapter 2.1, Class 9 Maths Chapter 2.1 solutions

Question 1.
Classify the decimal form of the given rational numbers into terminating and non-terminating recurring type.

Solution:
i. Denominator = 5 = 1 x 5
Since, 5 is the only prime factor denominator.
the decimal form of the rational number 135 will be terminating type.

ii. Denominator = 11 = 1 x 11
Since, the denominator is other than prime factors 2 or 5.
∴ the decimal form of the rational number 211 will be non-terminating recurring type.

iii. Denominator = 16
= 2 x 2 x 2 x 2
Since, 2 is the only prime factor in the denominator.
∴ the decimal form of the rational number 2916 will be terminating type.

iv. Denominator = 125
= 5 x 5 x 5
Since, 5 is the only prime factor in the denominator.
the decimal form of the rational number 17125 will be terminating type.

v. Denominator = 6
= 2 x 3
Since, the denominator is other than prime factors 2 or 5.
∴ the decimal form of the rational number 116 will be non-terminating recurring type.

Question 2.
Write the following rational numbers in decimal form.





Solution:
i. −57

ii. 911

iii. √5

iv. 12113

v. 298

Question 3.
Write the following rational numbers in pq form.

Solution:
i. Let x = 0.6˙ …(i)
∴ x = 0.666…
Since, one number i.e. 6 is repeating after the decimal point.
Thus, multiplying both sides by 10,
10x = 6.666…
∴ 10 x 6.6 …(ii)
Subtracting (i) from (ii),
10x – x = 6.6 – 0.6
∴ 9x = 6

ii. Let x = 0.37¯¯¯¯¯
∴ x = 0.3737…
Since, two numbers i.e. 3 and 7 are repeating after the decimal point.
Thus, multiplying both sides by 100,
100x = 37.3737……
∴ 100x = 37.37¯¯¯¯¯ ……(ii)
Subtracting (i) from (ii),
100x – x = 37.37¯¯¯¯¯ – 0.37¯¯¯¯¯
∴ 99x = 37

iii. Letx = 3.17¯¯¯¯¯ …(i)
∴ x = 3.1717…
Since, two numbers i.e. 1 and 7 are repeating after the decimal point.
Thus, multiplying both sides by 100,
100x = 317.1717…
∴ 100x= 317.17 …(ii)
Subtracting (i) from (ii),
100x – x = 317.17¯¯¯¯¯ – 3.17¯¯¯¯¯
∴ 99x = 314

iv. Let x = 15.89¯¯¯¯¯ …….. (i)
∴ x = 15.8989…
Since, two numbers i.e. 8 and 9 are repeating after the decimal point.
Thus, multiplying both sides by 100,
100x= 1589.8989…
∴ 100x = 1589.89¯¯¯¯¯ …(ii)
Subtracting (i) from (ii),
100x – x = 1589.89¯¯¯¯¯ – 15.89¯¯¯¯¯
∴ 99x = 1574

v. Let x = 2.514¯¯¯¯¯¯¯¯
∴ x = 2.514514…
Since, three numbers i.e. 5, 1 and 4 are repeating after the decimal point.
Thus, multiplying both sides by 1000,
1000x = 2514.514514…
1000x = 2514.514¯¯¯¯¯¯¯¯ ….(ii)
Subtracting (i) from (ii),
1000x – x = 2514.514¯¯¯¯¯¯¯¯ – 2.514¯¯¯¯¯¯¯¯
∴ 999x = 2512

Question 1.
How to convert 2.43 in pq form ? (Textbook pg. no. 20)
Solution:
Let x = 2.43
In 2.43, the number 4 on the right side of the decimal point is not recurring.
So, in order to get only recurring digits on the right side of the decimal point, we will multiply 2.43 by 10.
∴ 10x = 24.3 …(i)
∴ 10x = 24.333…
Here, digit 3 is the only recurring digit. Thus, by multiplying both sides by 10, 100x = 243.333…
∴ 100x= 243.3 …(ii)
Subtracting (i) from (ii),
100x – 10x = 243.3 – 24.3
∴ 90x = 219

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Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 2.1- Real Numbers

Download PDF: Maharashtra Board Solutions Class 9-Maths (Part 1): Chapter 2.1- Real Numbers PDF

Chapterwise Maharashtra Board Solutions Class 9 Maths :

Part 1

• Chapter 1.1- Sets
• Chapter 1.2- Sets
• Chapter 1.3- Sets
• Chapter 1.4- Sets
• Chapter 2.1- Real Numbers
• Chapter 2.2- Real Numbers
• Chapter 2.3- Real Numbers
• Chapter 2.4- Real Numbers
• Chapter 2.5- Real Numbers
• Chapter 3.1- Polynomials
• Chapter 3.2- Polynomials
• Chapter 3.3- Polynomials
• Chapter 3.4- Polynomials
• Chapter 3.5- Polynomials
• Chapter 3.6- Polynomials
• Chapter 4.1- Ratio and Proportion
• Chapter 4.2- Ratio and Proportion
• Chapter 4.3- Ratio and Proportion
• Chapter 4.4- Ratio and Proportion
• Chapter 4.5- Ratio and Proportion
• Chapter 5.1- Linear Equations in Two Variables
• Chapter 5.2- Linear Equations in Two Variables
• Chapter 6.1- Financial Planning
• Chapter 6.2- Financial Planning
• Chapter 7.1- Statistics
• Chapter 7.2- Statistics
• Chapter 7.3- Statistics
• Chapter 7.4- Statistics
• Chapter 7.5- Statistics