Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(

Answer 1

0.72¯¯¯¯¯ can be represented as the decimal 0.727272..., where the repeating decimal pattern is 72. To convert this to a rational number in simplest form, we can let x = 0.727272...

Then, 100x = 72.727272..., which can be written as:

100x = 72 + 0.727272...
100x = 72 + x
99x = 72
x = 72/99

Therefore, 0.727272... as a rational number in simplest form is 72/99.