Question

Express 1.256 (bar on 56
) in the form p/q

Answer 1

$\textbf{ \huge{ Hello Mate! }}$

Let x = 1.2565656.......

Multiply 10 from x

10x = 12.565656.....

10x = 12 + 0.565656.....

[ Keep y = 0.565656...... __(1)

Multiply 100 from y

100y = 56.565656.... ___(2)

Subtracting (2) from (2)

99y = 56

y = 56 / 99 ]

10x = 12 + 56 / 99

10x = ( 12 × 99 + 56 ) / 99

10x = ( 1188 + 56 ) / 99

x = 1244 / 990

Note : 1. In mixed form, if digit with no bar is one then take 10, if two then 100 and so on.

2. In normal form like 0.5656.... then number of digits here are repeating are two so I nultiplied it with 100.

Have great future ahead!