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NCERT solutions Mathematics Textbook for Class 9 chapter 1 Number Systems

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Chapter 1 - Number Systems

Page 14

Write the following in decimal form and say what kind of decimal expansion each has :-

`(i) 36/100`

`(ii) 1/11`

`(iii) 4 1/8`

`(iv) 3/13`

`(v) 2/11`

`(vi) 329/400`

Q 1 | Page 14 |

You know that `1/7=0.bar142857.` Can you predict what the decimal expansions of `2/7, 3/7, 4/7, 5/7, 6/7`  are, Without actually doing the long division? If so, how?

[Hint : Study the remainders while finding the value of `1/7` carefully.]

Q 2 | Page 14 |

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

`(i) 0.bar6`

`(ii) 0.4bar7`

`(iii) 0.bar001`

Q 3 | Page 14 |

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

Q 4 | Page 14 |

What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.

Q 5 | Page 14 |

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?

Q 6 | Page 14 |

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

Q 7 | Page 14 |

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

Q 8 | Page 14 |

Classify the following numbers as rational or irrational :-

`(i) sqrt23`

`(ii) sqrt225`

(iii) 0.3796

(iv) 7.478478...

(v) 1.101001000100001...

Q 9 | Page 14 |

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