Question

please answer this question​

Answer 1

Topic

• Repeating Decimal

The subtraction between iterating decimals cancels each other out.

Solution

① Constructing a linear equation.

Let the given number be $x$.

$\implies x=3.4\overline{5}$

Let's multiply it by $10$,

$\implies 10x=34.\overline{5}$

then multiply by $100$.

$\implies 100x=345.\overline{5}$

② Subtraction between iterating decimals.

If we subtract each other,

$\implies 100x-10x=345.\overline{5}-34.\overline{5}$

$\implies 90x=311$

Now we are left with a linear equation.

$\implies x=\dfrac{311}{90}$

③ Conclusion

So, the number is $\dfrac{311}{90}$.

This is the required answer.

Answer 2

Answer :

Let x  = 3.45555 - (1)

》Periodicity = 1, so multiply by 10.

》Multiply (1) by 10.

10x = 34.555 - (2)

》Periodicity = 2, so multiply with 10.

》Multiply (2) by 10.

100x = 345.5555 - (3)

》Subtract (3) and (2).

100x = 345.5555

10x = 34.555

___________

90x = 311

x = 311/90

∴ Value of x is 311/90.