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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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

$x = \frac{297}{999} = \frac{11}{37}$ $color(magenta)(x=297/999=11/37$

Explanation:

$Equation 1:-$ $"Equation 1:-"$

$Let x be = 0.297$ $"Let " x " be" = 0.297$

$Equation 2:-$ $"Equation 2:-"$

$So, 1000 x = 297.297$ $"So", 1000x=297.297$

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

$1000 x - x = 297.297 - 0.297$ $1000x-x=297.297-0.297$

$999 x = 297$ $999x=297$

$x = \frac{297}{999} = \frac{11}{37}$ $color(magenta)(x=297/999=11/37$

$0 . ¯ ¯¯¯¯ ¯ 297 can be written as a rational number in the form \frac{p}{q} where q \neq 0 is \frac{11}{37}$ $0.bar 297 " can be written as a rational number in the form " p/q " where " q ne 0 " is" 11/37$

$~Hope this helps! :)$ $"~Hope this helps! :)"$

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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?

1 Answer

Explanation:

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