Question

write the following rationals in decimal form​

Answer 1

Please type the question completely.

Answer 2

Question:

Write the following Rationals in decimal form​ using Theorem 1.4.

(i) 13/25

(ii) 15/16

(iii) 23/ 2³$5^{5}$

(iv) 7218/3²5²

(v) 143/110

Step-by-step explanation:

Theorem 1.4: Let x = p/q be a rational number, such that the Prime factorisation of 'q' is of the form $2^n$ x $5^m$, where 'n' and 'm' are Non - Negative Integers. Then '$x$' has a decimal expansion which terminates.

(i) 13/25 = 13/5²

= 13/5² = 13 x 2²/2² x 5²

= 13 x 4/(2 x 5)² = 52/(10)²

= 0.52

(ii) 15/16 = 15/2 x 2 x 2 x 2

= 15/$2^4$

= 15 x $5^4$/$2^4$ x $5^4$

= 15 x 625/ (2 x 5$)^4$

= 9375/$10^4$

= 0.9375

(iii) 23/ 2³$5^{5}$

= 23 x 5/2³$5^{5}$

= 115/(2 x 5)³

= 115/10³ = 0.115

(iv) 7218/3²5²

= 802/5²

= 802 x 2²/2² x 5²

= 3208/(2 x 5)² = 3208/10²

= 0.3208

(v) 143/110

= 143/2 x 5 x 11

= 13/2 x 5 = 13/10

= 1.3

HOPE WHETHER THE QUESTIONS AND THEIR SOLUTIONS ARE CORRECT!