Come si converte 0.23 (3 ripetendo) come una frazione?

#0.23# con i #3# repeating can be written as #0.2dot3#, where the dot on top of the #3# means a repeating number or pattern of numbers.

#x = 0.2dot3#

#10x = 2.dot3#

#100x=23.dot3#

#90x = 100x - 10x#

#90x = 23.dot3 - 2.dot3#

#90x = 23 - 2 = 21#

#90x = 21#

#x = 21/90#

#= 7/30#