The decimal 0.297297 . . ., in which the sequence 297 repeats endlessly, is rational. Show that it is rational by writing it in the form p/q where p and q are intergers. Can i get help?

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Answer 1 · 2018-03-29T17:48:20

#color(magenta)(x=297/999=11/37#

#"Equation 1:-"#

#"Let " x " be" = 0.297#

#"Equation 2:-"#

#"So", 1000x=297.297#

#"Subtracting Eq. 2 from Eq. 1, we get:"#

#1000x-x=297.297-0.297#

#999x=297#

#color(magenta)(x=297/999=11/37#

#0.bar 297 " can be written as a rational number in the form " p/q " where " q ne 0 " is" 11/37#

#"~Hope this helps! :)"#