Question

Express in to simplest form fast in copy!!

Answer 1

1) let x = 0.40777777....
100x = 40.77777.....
- x = -0.40777....
99x = 40.37
x = 4037÷ 9900
× = 367÷900

2) let x = 1.323232323.....
100x = 132.3232323.....
-x = -1.3232323...
99x = 131
x = 131÷99

Answer 2

(1)

0.407(bar on 7) = 0.40777777

Multiply both sides by 100

= > 100x = 40.77777 ---- (1)

Multiply both sides by 1000

= > 1000x = 407.77777 ---- (2)

On solving (1) & (2), we get

= > 1000x - 100x = 407.77777 - 40.77777

= > 900x = 367

= > x = (367/900).

(2)

Given 1.323 = 1.323232323 --- (1)

Here, periodicity is 2.

= > Multiply both sides by 100

= > 100x = 132.3232 ---- (2)

On solving (2|) & (1), we get

= > 100x - x = 132.32323232 - 1.32323232

= > 99x = 131

= > x = 131/99.

Hope this helps!