Question

Express 0.6 + 0.47 in the form p/q where p and q are integers q are not equal to 0​

Answer 1

`0.6 + \bar 0.47 = (532)/(495)`

Explanation:

Given

`0.6 + \bar 0.47`

Required

Express as x/y

Let

`x = \bar 0.47`

This implies that:

`x = 0.4747` --- (1)

Multiply by 100

`100x = 47.4747` --- (2)

Subtract 1 from 2

`100x - x = 99x`

This gives

`47.4747 - 0.4747 = 47`

So:

`99x = 47`

Solve for x

`x = (47)/(99)`

This implies that:

`\bar 0.47 = (47)/(99)`

`0.6 + \bar 0.47` becomes

`0.6 + \bar 0.47 = 0.6 + (47)/(99)`

Express 0.6 as fraction

`0.6 + \bar 0.47 = (6)/(10) + (47)/(99)`

Take LCM and solve

`0.6 + \bar 0.47 = (99*6+10*47)/(990)`

`0.6 + \bar 0.47 = (1064)/(990)`

Simplify

`0.6 + \bar 0.47 = (532)/(495)`