Question

Identify a rational number among the following numbers: root25/6,root20/4,2.27bar,root2androot3

Answer 1

heya mate

the rational number among the following is 2.27bar because we know that all non terminating but recurring decimal expansion are rational numbers

here is the proof :

x = 2.272727....

100x= 227.2727.....

$subtracting$

100x - x = 227.2727...-2.2727...

99x = 225

$x = \frac{225}{99}$
hence it can be represi in the form of p/q where (q is not equal to 0)

so 2.27bar is a rational number