Question

$the \: decimal \: equivalent \: to \\ \frac{1}{10} + \frac{11}{100} + \frac{11}{1000} \\ a)11.11 \\ b)0.123 \\ c)0.321 \\ d)0.1111$


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Answer 1

Answer:

options C 0.321

Step-by-step explanation:

prefer to 9th class

Answer 2

⇝ Given :-

The numerator of a fraction is 1 less than the denominator.

If 1 is subtracted from the numerator, the fraction becomes 5/6

⇝ To Find :-

The Original Fraction.

⇝ Solution :-

For the Original Fraction Let,

Numerator = \large \rm xx

As The numerator of a fraction is 1 less than the denominator.

Therefore,

Denominator = \large \rm (x+1)(x+1)

So ,

\begin{gathered}\text{Original Fraction = } \frac{\text x}{\text x + 1} \\ \end{gathered}

Original Fraction =

x+1

x

❒ When 1 is subtracted from the numerator :

\begin{gathered}\text{Fraction Becomes : } \frac{\text x-1}{\text x + 1} \\ \end{gathered}

Fraction Becomes :

x+1

x−1

⏩ According To Question :

\begin{gathered}\bf \large\red{ \frac{ x - 1}{x + 1} = \frac{5}{6}} \\\end{gathered}

x+1

x−1

=

6

5

✧ On Cross Multiplying ;

\begin{gathered}:\longmapsto \rm 6(x - 1) = 5(x + 1) \\ \end{gathered}

:⟼6(x−1)=5(x+1)

\begin{gathered}:\longmapsto \rm 6x - 6 = 5x + 5 \\ \end{gathered}

:⟼6x−6=5x+5

\begin{gathered}:\longmapsto \rm 6x - 5x = 6 + 5 \\ \end{gathered}

:⟼6x−5x=6+5

\purple{ \large :\longmapsto \underline {\boxed{{\bf x =11} }}}:⟼

x=11

∴ Numerator of Fraction is 11 .

❒ As The numerator of a fraction is 1 less than the denominator.

\begin{gathered} \therefore \rm Denominator = Numerator + 1 \\ \end{gathered}

∴Denominator=Numerator+1

\begin{gathered}:\longmapsto \rm Denominator = 11 + 1 \\ \end{gathered}

:⟼Denominator=11+1

∴ Denominator of Fraction is 12 .

Therefore,

\begin{gathered}\large\underline{\pink{\underline{\frak{\pmb{Original \: Fraction = \frac{11}{12} }}}}} \\ \end{gathered}

OriginalFraction=

12

11

OriginalFraction=

12

11