express the decimal expression into rational numbers 1.2.327(327 in whole bar
Answers
Answer:
sorry I cannot do this but I will give u a related question .
if the question is Express the following decimal expression into rational numbers. (i) 0. ¯¯¯¯¯¯ 24 0.24¯ (ii) 2. ¯¯¯¯¯¯¯¯ 327 2.327¯ (iii) -5.132 (iv) 3.1 ¯ 7 3.17¯ (v) 17. ¯¯¯¯¯¯¯¯ 215 17.215¯ (vi) − 21.213 ¯
Step-by-step explanation:
answer:- i) 0. ¯¯¯¯¯¯ 24 0.24¯ Let x = 0. ¯¯¯¯¯¯ 24 0.24¯ = 0.24242424 … (1) (Here period of decimal is 2, multiply equation (1) by 100) 100x = 24.242424 … (2) (2) – (1) 100x – x = 24.242424… – 0.242424… 99x = 24 x = 24 99 2499 (ii) 2. ¯¯¯¯¯¯¯¯ 327 2.327¯ Let x = 2.327327327… (1) (Here period of decimal is 3, multiply equation (1) by 1000) 1000x = 2327.327… (2) (2) – (1) 1000x – x = 2327.327327… – 2.327327… 999x = 2325 x = 2325 999 2325999 (iii) -5.132 x = -5.132 = − 5132 1000 = − 1283 250 −51321000=−1283250 (iv) 3.1 ¯ 7 3.17¯ Let x = 3.1777 … (1) (Here the repeating decimal digit is 7, which is the second digit after the decimal point, multiply equation (1) by 10) 10x = 31.7777 … (2) (Now period of decimal is 1, multiply equation (2) by 10) 100x = 317.7777… (3) (3) – (2) 100x – 10x = 317.777… – 31.777… 90x = 286 x = 286 90 = 143 45 28690=14345 (v) 17. ¯¯¯¯¯¯¯¯ 215 17.215¯ Let x = 17.215215 … (1) 1000x = 17215.215215 … (2) (2) – (1) 1000x – x = 17215.215215… – 17.215… 999x = 17198 x = 17198 999 17198999 (vi) − 21.213 ¯ 7 −21.2137¯ Let x = -21.2137777… (1) 10x = -212.137777… (2) 100x = -2121.37777… (3) 1000x = -21213.77777… (4) 10000x = 212137.77777… (5) (Now period of decimal is 1, multiply equation (4) it by 10) (5) – (4) 10000x – 1000x = (-212137.7777…) – (-21213.7777…) 9000x = -190924 x = − 190924 9000Read more on Sarthaks.com - https://www.sarthaks.com/962391/express-the-following-decimal-expression-into-rational-numbers-bar-bar-327-iii-132-bar-bar