Question

If x = 1.23 ( bar on 23) and y = 12.3 ( bar on 3) find x+y.

Answer 1

hiii!!!

here's ur answer...

given x = 1.2323232323... and y = 12.333333...

first we will convert both x and y into rational number.

1. x = 1.23232323... -------(1)

multiplying both sides by 100.

100 × x = 100 × 1.23232323...

100x = 123.23232323... -------(2)

subtract equation (1) from equation (2)

100x - x = 123.23232323... - 1.23232323...

99x = 122

x = 122/99

2. y = 12.3333333... -------(1)

multiplying both sides by 10.

10 × x = 10 × 12.3333333...

10x = 123.3333333... --------(2)

subtract equation (1) from equation (2)

10x - x = 123.333333... - 12.3333333...

9x = 111

x = 111/9

therefore x + y = 122/99 + 111/9

= 122/99 + 1221/99

= 1343/99

hope this helps..!!

Answer 2

First we need to convert each nuber in fraction form to be more accurate.

$x=1. \overline{23}$

or we can expand that to get:

$x=1. 232323\overline{23}$...(i)

multiply by 100 on both sides

$100x=1 23.2323\overline{23}$...(ii)

subtract (i) from (ii)

99x=122

x=122/99

Similarly we can represent y into fraction form

$y=12. \overline{3}$

or we can expand that to get:

$y=12.33333\overline{3}$...(iii)

multiply by 10 on both sides

$10y=123.3333\overline{3}$...(iv)

subtract (iii) from (iv)

9y=111

y=111/9

Now we know accurate values of x and y so we can easily add them

x+y=122/99+111/9=1343/99=13.565656

Hence final answer is 1343/99 or $13. \overline{56}$