Come si converte 0.45 (45 ripetendo) in una frazione?

Scorciatoia: #(" write down the recurring digits")/("write a 9 for each recurring digit")#

Metodo lungo:

#"Let" x = 0.454545....#
# 100x = 45.454545..... " 2 recurring digits" rArr xx 100#

#99x = 45.000000..... " the decimals all subtract to 0"#

#x = 45/99#

Semplifica se possibile.