Question

please answer.(v),(vi)(vii),(viii)

Answer 1

hiii!!!

here's Ur answer...

(v) 0.324324324324...

let x be = 0.324324324... --------(1)

multiplying both sides by 1000 since e numbers are repeating.

1000 × x = 1000 × 0.324324324...

1000x = 324.324324324... --------(2)

subract equation (1) from equation (2)

1000x - x = 324.324324324... - 0.324324324...

999x = 324

x = 324/999

x = 108/333

x = 36/111

x = 12/37

(vi) 0.177777777...

let x be = 0.177777777... --------(1)

multiplying both sides by 10 since 1 number is repeating.

10 × x = 10 × 0.17777777...

10x = 1.7777777... --------(2)

subract equation (1) from equation (2)

10x - x = 1.77777777... - 0.17777777...

9x = 1.6

x = 1.6/9

(vii) 0.54444444...

let x be = 0.54444444... --------(1)

multiplying both sides by 10 since one number is repeating.

10 × x = 10 × 0.544444444...

10x = 5.44444444... --------(2)

subract equation (1) from equation (2)

10x - x = 5.44444444... - 0.54444444...

9x = 4.9

x = 4.9/9

(viii) 0.163636363...

let x be = 0.163636363... --------(1)

multiplying both sides by 100 since 2 numbers are repeating.

100 × x = 100 × 0.163636363...

100x = 16.363636363... --------(2)

subract equation (1) from equation (2)

100x - x = 16.363636363... - 0.16363636363...

99x = 16.2

x = 16.99

hope this helps..!!