Question

the value of 3.555555___ in p/q form is ____​

Answer 1

Given Question -

the value of 3.555555.... in p/q form is ____ .

Required Answer -

3.(5) bar

${\sf{:\implies 3 .\bar{5}}}$

Let 3.555555... be x

${\sf{:\implies 3.555555...=x}}\: \: \: ...(1)$

Multiplying both side with 10

${\sf{:\implies 35.5555...=10 x}} \: \: \: ...(2)$

Now subtract (i) from (ii)

As we know that , 5555... Is non terminating so there will be no change if we write it as zero on subtracting .

${\sf{:\implies (35.5555..)-(3.5555..)=(10x)-( x)}}$

${\sf{:\implies 32=9 x}}$

${\sf{:\implies x = \bold{\dfrac{32}{9} }}}$

If you will convert it again into decimal then you will get result as 0.13(8)bar only

$\begin{gathered} \begin{gathered}\begin{gathered} \underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\ \end{gathered} \end{gathered} \end{gathered}$

the value of 3.555555.... in p/q form is 32/9 .

Answer 2

Answer: x = 32/9

Explanation:

Let, x = 3.5 bar

Now,

10x = 35.5 bar

=> 10x = 32 + 3.5 bar

But, 3.5 bar = x,

∴ 10x = 32 + x

=> 10x - x = 32

=> 9x = 32

=> x = 32/9

ALITER:

We can express 3.5 bar as 3 + 0.5 bar

Now,

0.5 bar can be written as 5/9

(N.B.: As bar is on one digit, there's only one 9 in denominator. In case of bar over two digit, make denominator 99. Similarly for 3 digit, denominator should be 999. Example, 0."352" bar = 352/999.)

Therefore, 3 + 5/9 = 32/9.