Q4 of 23 Page 1

Complete the following:
(i) Every point on the number line corresponds to a _____________  numberwhich may be either  _____________ or _____________.
(ii) The decimal form of an irrational number is neither _____________  or_____________.
(iii) The decimal representation of the rational number https://static.philoid.co/ncertusercontent/solutions/user_files/63094/15039/images/extra-1_files/Image3058.gif is _____________.
(iv) 0 is  _____________  number. [Hint: a rational /an irrational]


(i) Every point on the number line corresponds to a real number which may be either rational or irrational.
(ii) The decimal form of an irrational number is neither recurring or terminating.
(iii) The decimal representation of the rational number https://gs-post-images.grdp.co/user_files/63094/15039/images/extra-1_files/Image3059.gif is 0.296296…
(iv) 0 is a rational number. (since it can be represented in the form p/q, 0/q=0)

More from this chapter

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2

If a is a positive rational number and n is a positive integer greater than 1,prove that a n is a rational number.

3

Find three rational numbers lying between 0 and 0.1. Find twenty rationalnumbers between 0 and 0.1. Give a method to determine any number ofrational numbers between 0 and 0.1.

5
Which of the following rational numbers have the terminating decimalrepresentation?
(i)3/5             (ii)7/20                   (iii)2/13
(iv) 27/40        (v)133/125            (vi)23/7
[Making use of the result that a rational number p/q where p and q have nocommon factor(s) will have a terminating representation if and only if theprime factors of q are 2's or 5's or both. 6

You have seen that √2 is not a rational number. Show that

2  +  √2 is not a rational number.