Question

write 23.426426... in the form of p/q

Answer 1

23.426426 in p/q

= 23.426426 /1000000

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Answer 2

Answer :

Given = 23.426426....

here, 426 is repeating

to write 23.426426... in the form of p/q

=> let x = 23.426426... (1)

multiply both sides of eq. (1) with 1000

(we multiplied with 1000 because 3 digits are repeating)

$\: 1000x = 23426.426426... \: \: \: \: \: (2) \\ \\ now \: subtract \: eq. \: (2) \: from \: (1) \\ \\ = > \: 1000x - x = 23426.426426... - 23.426426... \\ \\ = > \: 999x = 23403 \\ \\ x = \frac{23403}{999} \\ \\ x = \frac{7801}{333} \\ \\ therefore \: 23.426426... \: in \: the \: form \: of \: \frac{p}{q } \\ \\ = > \: \frac{7801}{333}$

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