Real Numbers 1. Euclid’s Algorithm for HCF: Euclid, a Greek mathematician, devised an interesting method to find the HCF of two numbers. This method is known as Euclid’s Algorithm. An algorithm is a stepwise process to solve a problem. Steps taken to find the HCF of two numbers are as under: 1. Identify the greater …
EXERCISE 1.4 1. 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 : Sol. We know that if the denominator of a rational number has no prime factors other than 2 or 5, then it is expressible as a terminating, …
EXERCISE 1.3 Sol. Let us assume, to the contrary, that is rational.Now, let , where a and b are coprime and Squaring on both sides, we get => … (1) This shows that is divisible by 5.It follows that a is divisible by 5 … (2)=> a = 5m for some integer m. Substituting a …
EXERCISE 1.2 1. Express each number as a product of its prime. Factors :(i) 140 (ii) 156 (iii) 3825(iv) 5005 (v) 7429 Sol. (i) We use the division method as shown below : : – 140 = 2 × 2 × 5 x 7 =x5x7 (ii) We use the division method as shown below: : …
EXERCISE I.I 1. Use Euclid’s division algorithm to find the HCF of : (i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255 Sol. (i) We have, Dividend = 225 and Divisor = 135The process can be exhibited as under : Hence, HCF (135, 225) = 45(ii) We have, Dividend = 38220 and …