Question

answer pljjj........ ​

Answer 1

Answer:4.09/9

Step-by-step explanation:

x = 0.45444—-1

multiplying by 10 on both sides of eq -1

10x = 4.5444.    (Subtracting)

  x =  0.4544     -

————————

9x =  4.0900

x= 4.09/9

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Answer 2

Question :-

Express 0.454444---- in the form of p/q ( p by q ) ?

Answer :-

Given :-

0.454444------

Required to find :-

• p/q form of the given number

Solution :-

Given an non- terminating recurring decimal ,

0.45444 - - - - -

So,

Let's find the period and periodicity

Period = 4

Periodicity = 1

Hence,

$\tt{Let\; x = 0.45444 - - - - }{\longrightarrow{\red{equation - 1 }}}$

Since the periodicity is 1 .

Multiply with 10 on both sides

10 ( x ) = 10 ( 0.45444 - - - - )

$\tt{ 10x = 4.54444 - - - - }{\longrightarrow{\orange{equation - 2}}}$

Now,

$\textsf{ Subtract }{\mathsf{\red{\;equation \; 1\;}}}{\tt{\blue{from}}}{\tt{\green{\;equation\;2}}}$

So,

10x = 4.54444 - - - -

1x = 0.45444 - - - -

$\rule{200}{6}$

9x = 4. 09000 - - - -

$\implies{ x = \dfrac{4.09}{9}}$

$\implies{ x = \dfrac{4.09}{9} \times \dfrac{100}{100}}$

$\implies{ x = \dfrac{ 409 }{ 900 }}$

Therefore,

$\boxed{\large{\rm{0.45}{\overline{4}}{\; = \; \dfrac{409}{900}}}}$

Points to remember :-

Period refers to the digit which is repeating .

For example :

Find period of 5.4444 - - - ?

Answer :

Here, period = 4

Since that digit is repeating

Periodicity refers to the number of digits repeating .

For example :-

Find period of 1.323232 - - - - ?

Answer :-

Periodicity = 2

Because no. of digits which are repeating are 2 .

Depending upon on the periodicity we should multiply the equation .

Similarly,

Only an non - terminating repeating decimal can only be converted into p/q form .