Question

Express 0.407(bar on 7 )in the form p/q.

Answer 1

$\textbf{Given:}\;0.40\overline{7}$

$\textbf{To find:}$

$\dfrac{p}{q}\;\text{form of}\;0.40\overline{7}$

$\textbf{Solution:}$

$\text{Let}\;x=0.40\overline{7}$

$\implies\,x=0.4077777777777.....$......(1)

$\text{Multiply bothsides of (1) by 100, we get}$

$\implies\,100x=40.77777777777.....$......(2)

$\text{Multiply bothsides of (1) by 1000, we get}$

$\implies\,1000x=407.77777777777.....$......(3)

$\text{Subtract (2) from (3), we get}$

$900x=367$

$\implies\bf\,x=\dfrac{367}{900}$

$\therefore\textbf{The \bf\dfrac{p}{q} of \bf0.40\overline{7} is \bf\dfrac{367}{900} }$

Find more:

Express 5.25bar in p/q form where q not equal to 0 p and q are co-primes

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Represent 3.67777777 in rational form

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Answer 2

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0.407

Let x = 0.407

=> x = 0.407777....... ... (1)

=> 1000x = 407.7777........ .. (2)

=> Subtract (1) from (2)

=>1000x-x = 407.777....... - 0.40777.......

=> 999x = 407

$\: \: \: \: = > x = \frac{407}{999}$

$\huge{\mathtt{\red{N}\pink{O}\green{T}\blue{E}\purple{:}\orange{-}}}\huge$

Dark colour of 7 in first two lines represent that there is bar on 7

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