Question

convert the 0.284bar
decimals into p/q form.​

Answer 1

GIVEN :-

$\implies \bf0. \overline{284}$

TO FIND :-

$\implies \bf0. \overline{284} \: \: in \: the \: form \: of \: \dfrac{p}{q}$

SOLUTION :-

$\to \bf \: let \: x \: = 0. \overline{284} \red{ \bf \: \: ...............(1)}$

Multiply 1000 on both the sides,

$\to \bf \: 1000x = 284. \overline{284} \red{ \: ...............(2)}$

$\boxed{ \huge \bf \red{(2) - (1)}}$

$\to \bf \: 1000 \: \: x = 284. \overline{284} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \: \: \bf x = 0. \overline{284} \: \: \: \: \: \: } \\ \to \: \: \: \: \: \: \: \bf \: 99 \: x = 284 \\ \\ \to \boxed{ \red{ \bf \: x \: = \dfrac{284}{999}}}$

Hence the required answer is 284/999

EXTRA INFORMATION :-

➵ Rational number :- Any number which can be expressed in the form of p/q where p and q are integers and q ≠ 0.

Example :- 3/5, 4/7, 0/6

➵ Natural numbers :- All counting numbers are called natural numbers .

Example :- 1, 2, 3, 4, 5.............∞