Express each of following as a vulgar fraction in simplest form : (i) 0.5 (ii) 0.43 (iii) 0.158 (iv) 1.3 (v) 4.17 (vi) 0.12 (vii) 0.136 (viii) 1.57

Question

KnowledgeBoat · Accepted Answer

(i) Let x = . ⇒ x = 0.555.. ...........(1) ⇒ 10x = 5.555.. ..........(2) On subtracting (1) from (2), we get : ⇒ 10x - x = 5.555... - 0.555... ⇒ 9x = 5 ⇒ x = Hence, . (ii) Let x = . ⇒ x = 0.434343.. .........(1) ⇒ 100x = 43.4343.. ........(2) On subtracting (1) from (2), we get : ⇒ 100x - x = 43.4343.... - 0.4343...... ⇒ 99x = 43 ⇒ x = Hence, . (iii) Let x = ⇒ x = 0.158158.. ......(1) ⇒ 1000x = 158.158158.. ......(2) On subtracting (1) from (2), we get : ⇒ 1000x - x = 158.158158.... - 0.158158..... ⇒ 999x = 158 ⇒ x = Hence, . (iv) Let x = ⇒ x = 1.3333.. ......(1) ⇒ 10x = 13.333.. ......(2) On subtracting (1) from (2), we get : ⇒ 10x - x = 13.333.. - 1.333.. ⇒ 9x = 12 ⇒ x = ⇒ x = Hence, . (v) Let x = ⇒ x = 4.1717.. ........(1) ⇒ 100x = 417.1717.. .......(2) On subtracting (1) from (2), we get : ⇒ 100x - x = 417.1717..... - 4.1717..... ⇒ 99x = 413 ⇒ x = Hence, . (vi) Let x = ⇒ x = 0.1222.. ...........(1) ⇒ 100x = 12.222...(ii) On subtracting (i) from (ii), we get ⇒ 99x = 12 ⇒ x = ⇒ x = ⇒ x = Hence, 0.12... = . (vii) Let x = ⇒ x = 0.13636.. ...........(1) ⇒ 10x = 1.3636.. ...........(2) ⇒ 1000x = 136.3636.. ...........(3) On subtracting (2) from (3), we get ⇒ 1000x - 10x = 136.3636.. - 1.3636.. ⇒ 990x = 135 ⇒ x = ⇒ x = ⇒ x = Hence, . (viii) Let x = . ⇒ x = 1.5777.. ...........(1) ⇒ 10x = 15.777.. ...........(2) ⇒ 100x = 157.7777.. ...........(3) On subtracting (i) from (iii), we get ⇒ 100x - 10x = 157.7777.. - 15.777...... ⇒ 90x = 142 ⇒ x = ⇒ x = ⇒ x = Hence, .

Mathematics

Express each of following as a vulgar fraction in simplest form : (i) 0.5 (ii) 0.43 (iii) 0.158 (iv) 1.3 (v) 4.17 (vi) 0.12 (vii) 0.136 (viii) 1.57

Rational Irrational Nos

Related Questions