What can you say about the prime factorizations of the denominators of

1.	What can you say about the prime factorizations of the denominators of the following rational?(i) 43.123456789(ii) \(43.\overline{123456789}\)(iii) \(27.\overline{142857}\)(iv) 0.120120012000120000…
Answer» (i) 43.123456789 \(\frac{43123456789}{100000000}\) = \(\frac{43123456789}{2^9\times 5^9}\) Since Prime factorization of the denominator is in the form 2^m x 5ⁿ, where m, n are non -negative integers. (ii) Since \(43.\overline{123456789}\) has non - terminating repeating decimal expression, therefore Prime factorization of the denominator contains factors other than 2 or 5. (iii) Since \(27.\overline{142857}\) has non - terminating repeating decimal expression, therefore Prime factorization of the denominator contains factors other than 2 or 5. (iv) Since \(27.\overline{142857}\) has non - terminating repeating decimal expression, therefore Prime factorization of the denominator contains factors other than 2 or 5.

What can you say about the prime factorizations of the denominators of the following rational?(i) 43.123456789(ii) \(43.\overline{123456789}\)(iii) \(27.\overline{142857}\)(iv) 0.120120012000120000…

Answer»

(i) 43.123456789

\(\frac{43123456789}{100000000}\) = \(\frac{43123456789}{2^9\times 5^9}\)

Since Prime factorization of the denominator is in the form 2^m x 5ⁿ, where m, n are non -negative integers.

(ii) Since \(43.\overline{123456789}\) has non - terminating repeating decimal expression, therefore

Prime factorization of the denominator contains factors other than 2 or 5.

(iii) Since \(27.\overline{142857}\) has non - terminating repeating decimal expression, therefore

Prime factorization of the denominator contains factors other than 2 or 5.

(iv) Since \(27.\overline{142857}\) has non - terminating repeating decimal expression, therefore

Prime factorization of the denominator contains factors other than 2 or 5.