EXERCISE - 1.2

1. Express each of the following numbers as a product of its prime factors.

(i) 140 (ii) 156 (iii) 3825 (iv) 5005 (v) 7429

2. Find the LCM and HCF of the following integers by the prime factorization method.

(i) 12, 15 and 21 (ii) 17, 23, and 29 (iii) 8, 9 and 25 (iv) 72 and 108 (v) 306 and 657

3. Check whether 6n can end with the digit 0 for any natural number n.

4. Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers

5. How will you show that (17 × 11 × 2) + (17 × 11 × 5) is a composite number? Explain.

6. What is the last digit of 6100

Now, let us use the Fundamental Theorem of Arithmetic to explore real numbers further. First, we apply this theorem to find out when the decimal from of a rational number is terminating and when it is non-terminating, repeating. Second, we use it to prove the irrationality of many numbers such as √2 , √3 and √5 .

1.2.1 RATIONAL NUMBERS AND THEIR DECIMAL EXPANSIONS

Till now we have discussed some properities of integers. How can you find the preceeding or the succeeding integers for a given integer? You might have recalled that the difference between an integer and its preceeding or succeding integer is 1. And by this property only you might have found required integers.

In calss IX, you learned that the rational numbers would be in either a terminating decimal form or a non-terminating, repeating decimal form. In this section, we are going to consider arational number, say p/q (q ¹ 0) and explore exactly when the number p/q is a terminatingdecimal, and when it is a non-terminating repeating (or recurring) decimal. We do so by considering certain examples

Let us consider the following terminating decimals.
(i) 0.375    (ii) 1.04    (iii) 0.0875     (iv) 12.5



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