BSEB Class 9 Maths Chapter 1 Number Systems Ex 1.3 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.3 Book Answers |

## Bihar Board Class 9th Maths Chapter 1 Number Systems Ex 1.3 Textbooks Solutions PDF

Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.3 Books Solutions with Answers are prepared and published by the Bihar Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of BSEB Class 9th Maths Chapter 1 Number Systems Ex 1.3 Books Answers Solutions, then you are in the right place. Here is a complete hub of Bihar Board Class 9th Maths Chapter 1 Number Systems Ex 1.3 solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.3 Textbooks. These Bihar Board Class 9th Maths Chapter 1 Number Systems Ex 1.3 Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Bihar Board.## Bihar Board Class 9th Maths Chapter 1 Number Systems Ex 1.3 Books Solutions

Board | BSEB |

Materials | Textbook Solutions/Guide |

Format | DOC/PDF |

Class | 9th |

Subject | Maths Chapter 1 Number Systems Ex 1.3 |

Chapters | All |

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## BSEB Class 9th Maths Chapter 1 Number Systems Ex 1.3 Textbooks Solutions with Answer PDF Download

Find below the list of all BSEB Class 9th Maths Chapter 1 Number Systems Ex 1.3 Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:## BSEB Bihar Board Class 9th Maths Solutions 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) 36100

(ii) 111

(iii) 418

(iv) 211

(v) 211

(vi) 329400

Solution:

(i) 36100 = 0.36, terminating.

(ii) By long division, we have

∴ 111 = 0.090909 = 0.09⎯⎯⎯⎯⎯⎯, non-terminating and repeating.

(iii) 418 = 4×8+18 = 338

By long division, we have

(iv) By long division, we have

∴311 = 0.23076923… = 0.230769⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯, non-terminating and repeating.

(v) By long division, we have

∴ 211 = 0.181818… = 0.18⎯⎯⎯⎯⎯⎯, non-terminating and repeating.

(vi) By long division, we have

Question 2.

You know that 17 = 0.142857⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯. Can you predict what the decimal expansions of 27, 37, 47, 57, 67 are, without actually doing the long division? If so, how?

Solution:

Yes. All of the above will have repeating decimals which are permutations of 1, 4, 2, 8, 5, 7.

For example, here

To find 27, locate when the remainder becomes 2 and respective quotient (here it is 2), then write the, new quotient beginning from there (the arrows drawn in the above division) using the repeating digits 1, 4, 2, 8, 5, 7.

Question 3.

Express the following in the form 𝑝𝑞, where p and q are integers and q ≠ 0.

(i) 0.6¯

(ii) 0.47¯

(iii) 0.001¯

Solution:

(i) Let x = 0.6¯

Then, x = 0.666 … (1)

Here, we have only one repeating digit. So, we multiply both sides of (1) by 10 to get

10x = 6.66 … (2)

Subtracting (1) from (2), we get

10x – x = (6.66…) – (0.66…)

⇒ 9x = 6 ⇒ x = 23

Hence, 0.6¯ = 23

(ii) Let x = 0.47¯

Clearly, there is just one digit on the right side of the decimal point which is without bar. So, we multiply both sides by x so that only the repeating decimal is left on the right side of the decimal point.

∴ 10x = 4.7¯

⇒ 10x = 4 + 0.7¯

⇒ 10x = 4 + 79

Rule :

- Write the number without decimal point as numerator.
- Write as many 9’s as there are different repeating digits for the denominator.

For example : 0.7¯ = 79, 0.35⎯⎯⎯⎯⎯⎯ = 3599 etc.

Aliter:

Let x = 0.47¯ = 0.4777 …

∴ 10x = 4.777 …. (1)

and 100x = 47.777 …. (2)

Subtracting (1) from (2), we get

100x – 10x = (47.777…) – (4.777…)

⇒ 90x = 43 ⇒ x = 4390

Hence, 0.47¯ = 4390

(iii) Let x = 0.001⎯⎯⎯⎯⎯⎯⎯⎯⎯

⇒ x = 0.001001001 … (1)

Here, we have three repeating digits after the decimal point. So, we multiply (1) by 10³ = 1000, we get

1000x = 1.001001 … (2)

Subtracting (1) from (2), we get

1000x – x = (1001001 …) – (0.001001…)

⇒ 999x = 1 ⇒ x = 1999

Hence, 0.001⎯⎯⎯⎯⎯⎯⎯⎯⎯1999

Question 4.

Express 0.99999 …. in the form 𝑝𝑞. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

Solution:

Let x = 0.9999 … (1)

Here, we have only one repeating digit. So, we multiply both sides of (1) by 10 to get

10x = 9.999 …(2)

Subtracting (1) from (2), we get

10x – x = (9.999…) – (0.999…)

⇒ 9x = 9 ⇒ x = 1

Hence, 0.9999… = 1

Since 0.9999… goes on forever. So, there is no gap between 1 and 0.9999… and hence they are equal.

Question 5.

What can the maximum number of digits be in the repeating block of digits in the decimal expansion 117? Perform the division to check your answer.

Solution:

We have

∴ The maximum number of digits in the quotient while computing 117 are 15.

Question 6.

Look at several examples of rational numbers in the form 𝑝𝑞(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?

Solution:

Consider several rational numbers in the form 𝑝𝑞 (q ≠ 0), where p and q are integers with common factors other than 1 and having terminating decimal representation.

Let the various such rational numbers be 12, 14, 78, 3725, 8125, 1720, 3116 etc.

In all cases, we think of the natural number which when multipled by their respective denominators gives 10 or a power of 10.

We have seen that those rational numbers whose denominators when multiplied by a suitable integer produce a power of 10 are expressible in the finite decimal form. But this can always be done only when the denominator of the given rational number has either 2 or 5 or both of them as the only prime factors. Thus, we obtain the following property :

If the denominator of a rational number in standard form has no prime factors other than 2 or 5, then and only then it can be represented as a terminating decimal.

Question 7.

Write three numbers whose decimal expansions are non-terminating non-recurring.

Solution:

Three numbers whose decimal representations are non-terminating and non-repeating are 2‾√, 3‾√ and 5‾√ or we can say 0.100100010001…, 0.20200200020002… and .003000000003…

Question 8.

Find three different irrational numbers between the rational numbers 57 and 911.

Solution:

We have

Thus, three different irrational numbers between 57 and 911 are

0. 75075007500075000075…, 0.767076700767000… and 0.80800800080000…

Question 9.

Classify the following numbers as rational or irrational :

(i) 23‾‾‾√

(ii) 225‾‾‾‾√

(iii) 0.3796

(iv) 7.478498 …

(v) 1.101001000100001…

Solution:

(i) 23‾‾‾√ is an irrational number as 23 is not a perfect square.

(ii)

Thus, 15 is a rational number.

(iii) 0.3796 is a rational number as it is terminating decimal.

(iv) 7.478478… is non – terminating but repeating, so, it is a rational number.

(v) 1.101001000100001… is non-terminating and non-repeating so, it is an irrational number.

## BSEB Textbook Solutions PDF for Class 9th

- BSEB Class 9 Textbook Solutions PDF: Download Bihar Board STD 9th Book Answers
- BSEB Class 9 Maths Textbook Solutions PDF: Download Bihar Board STD 9th Maths Book Answers
- BSEB Class 9 Maths Chapter 1 Number Systems Ex 1.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.1 Book Answers
- BSEB Class 9 Maths Chapter 1 Number Systems Ex 1.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.2 Book Answers
- BSEB Class 9 Maths Chapter 1 Number Systems Ex 1.3 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.3 Book Answers
- BSEB Class 9 Maths Chapter 1 Number Systems Ex 1.4 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.4 Book Answers
- BSEB Class 9 Maths Chapter 1 Number Systems Ex 1.5 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.5 Book Answers
- BSEB Class 9 Maths Chapter 1 Number Systems Ex 1.6 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 1 Number Systems Ex 1.6 Book Answers
- BSEB Class 9 Maths Chapter 2 Polynomials Ex 2.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 2 Polynomials Ex 2.1 Book Answers
- BSEB Class 9 Maths Chapter 2 Polynomials Ex 2.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 2 Polynomials Ex 2.2 Book Answers
- BSEB Class 9 Maths Chapter 2 Polynomials Ex 2.3 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 2 Polynomials Ex 2.3 Book Answers
- BSEB Class 9 Maths Chapter 2 Polynomials Ex 2.4 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 2 Polynomials Ex 2.4 Book Answers
- BSEB Class 9 Maths Chapter 2 Polynomials Ex 2.5 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 2 Polynomials Ex 2.5 Book Answers
- BSEB Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 3 Coordinate Geometry Ex 3.1 Book Answers
- BSEB Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 3 Coordinate Geometry Ex 3.2 Book Answers
- BSEB Class 9 Maths Chapter 3 Coordinate Geometry Ex 3.3 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 3 Coordinate Geometry Ex 3.3 Book Answers
- BSEB Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 4 Linear Equations in Two Variables Ex 4.1 Book Answers
- BSEB Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 4 Linear Equations in Two Variables Ex 4.2 Book Answers
- BSEB Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.3 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 4 Linear Equations in Two Variables Ex 4.3 Book Answers
- BSEB Class 9 Maths Chapter 4 Linear Equations in Two Variables Ex 4.4 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 4 Linear Equations in Two Variables Ex 4.4 Book Answers
- BSEB Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry Ex 5.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 5 Introduction to Euclid’s Geometry Ex 5.1 Book Answers
- BSEB Class 9 Maths Chapter 5 Introduction to Euclid’s Geometry Ex 5.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 5 Introduction to Euclid’s Geometry Ex 5.2 Book Answers
- BSEB Class 9 Maths Chapter 6 Lines and Angles Ex 6.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 6 Lines and Angles Ex 6.1 Book Answers
- BSEB Class 9 Maths Chapter 6 Lines and Angles Ex 6.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 6 Lines and Angles Ex 6.2 Book Answers
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- BSEB Class 9 Maths Chapter 7 Triangles Ex 7.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 7 Triangles Ex 7.1 Book Answers
- BSEB Class 9 Maths Chapter 7 Triangles Ex 7.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 7 Triangles Ex 7.2 Book Answers
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- BSEB Class 9 Maths Chapter 7 Triangles Ex 7.5 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 7 Triangles Ex 7.5 Book Answers
- BSEB Class 9 Maths Chapter 8 Quadrilaterals Ex 8.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.1 Book Answers
- BSEB Class 9 Maths Chapter 8 Quadrilaterals Ex 8.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 8 Quadrilaterals Ex 8.2 Book Answers
- BSEB Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.1 Book Answers
- BSEB Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.2 Book Answers
- BSEB Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.3 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.3 Book Answers
- BSEB Class 9 Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 9 Areas of Parallelograms and Triangles Ex 9.4 Book Answers
- BSEB Class 9 Maths Chapter 10 Circles Ex 10.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 10 Circles Ex 10.1 Book Answers
- BSEB Class 9 Maths Chapter 10 Circles Ex 10.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 10 Circles Ex 10.2 Book Answers
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- BSEB Class 9 Maths Chapter 10 Circles Ex 10.6 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 10 Circles Ex 10.6 Book Answers
- BSEB Class 9 Maths Chapter 11 Constructions Ex 11.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 11 Constructions Ex 11.1 Book Answers
- BSEB Class 9 Maths Chapter 11 Constructions Ex 11.2 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 11 Constructions Ex 11.2 Book Answers
- BSEB Class 9 Maths Chapter 12 Heron’s Formula Ex 12.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 12 Heron’s Formula Ex 12.1 Book Answers
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- BSEB Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 13 Surface Areas and Volumes Ex 13.1 Book Answers
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- BSEB Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.9 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 13 Surface Areas and Volumes Ex 13.9 Book Answers
- BSEB Class 9 Maths Chapter 14 Statistics Ex 14.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 14 Statistics Ex 14.1 Book Answers
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- BSEB Class 9 Maths Chapter 14 Statistics Ex 14.4 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 14 Statistics Ex 14.4 Book Answers
- BSEB Class 9 Maths Chapter 15 Probability Ex 15.1 Textbook Solutions PDF: Download Bihar Board STD 9th Maths Chapter 15 Probability Ex 15.1 Book Answers

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