Question

give step by step solution i will give 20 points .the correct answer is 3221 upon 990
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Answer 1

Question.

Express $3.2\overline{53}$ as a fraction in the form $\dfrac{x}{y}$, $x,y\in \mathbb{I}$ (It means integer values.) and $y\neq 0$.

Hint.

Let $a=3.2\overline{53}$, so that $10a=32.\overline{53}$ and $1000a=3253.\overline{53}$.

When we subtract the same recurring part on two numbers $1000a$ and $10a$, the recurring part is removed, and we are left with a linear equation $1000a-10a=3253-32$.

Solution.

$1000a-10a=3253-32$

$\implies 990a=3221$

$\implies \boxed{a=\dfrac{3221}{990}}$

Solve more problems.

Express $0.\overline{9}$ as an irreducible fraction.

(Answer: $\dfrac{1}{1}$)

Answer 2

Answer:

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$3.2\overline{53}$ as a fraction in the form $\dfrac{x}{y}$, $x,y\in \mathbb{I}$ (It means integer values.) and $y\neq 0$.

$1000a-10a=3253-32$

$\implies 990a=3221$

$\implies \boxed{a=\dfrac{3221}{990}}$