Real Numbers Te...

If $$d$$ is the $$HCF$$ of 45 and 27, then $$x, y$$ satisfying $$d=27x+45y$$ are :

Use Euclid's division lemma to find the HCF : 

Use Euclid's division lemma to find the $$HCF$$ of the following numbers:

The decimal expansion of the rational number $$\dfrac {33}{2^2\cdot 5}$$ will terminate after:

Without doing any actual division, find which of the following rational numbers have terminating decimal representation :
(i) $$\displaystyle \dfrac{7}{16}$$ (ii) $$\displaystyle \dfrac{23}{125}$$
(iii) $$\displaystyle \dfrac{9}{14}$$ (iv) $$\displaystyle \dfrac{32}{45}$$
(v) $$\displaystyle \dfrac{43}{50}$$ (vi) $$\displaystyle \dfrac{17}{40}$$
(vii) $$\displaystyle \dfrac{61}{75}$$ (viii) $$\displaystyle \dfrac{123}{250}$$

The given pair of numbers $$ 231, 396$$ are __________ .

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
$$\dfrac {29}{343}$$

$$\frac {23}{2^35^2}$$

If these numbers form positive odd integer 6q+1, or 6q+3 or 6q+5 for some q then q belongs to:

 The square of any positive odd integer for some integer $$ m$$ is of the form