Question

Convert 0.016 into rational number if ther is bar over 16

Answer 1

x=0.016

10x =0.16 ------------(1)

1000x=16.16--------(2)

subtracting eq.(1) from eq.(2) we get,

1000x = 0.16

- 10x =16.16

----------------------

990x=16

----------------------

x =16/990 or 8/495

Answer 2

Answer:

The required rational number is $\frac{4}{225}$.

Step-by-step explanation:

Step 1 of 3

Consider the given number as follows:

$0.0\overline{16}$

or,

$0.0\overline{16}=0.016161...$

Now, let $x=0.0\overline{16}$. Then,

$x=0.0161616...$ . . . . . (1)

Step 2 of 3

Multiply both the sides of the equation (1) by the number $10$.

⇒ $10x=10\times 0.0161616...$

⇒ $10x=0.1616...$ . . . . . (2)

Now, multiply both the sides of the equation (1) by the number $1000$.

⇒ $1000x=1000\times 0.0161616...$

⇒ $1000x=16.1616...$ . . . . . (3)

Step 3 of 3

Computing the value of $x$.

Subtract the equation (2) from the equation (3) as follows:

⇒ $1000x-10x=16.1616...-0.1616...$

⇒ $900x=16$

⇒ $x=\frac{16}{900}$

On simplifying, we get

$x=\frac{4}{225}$

Therefore, the conversion of $0.0\overline{16}$ into the rational number is $\frac{4}{225}$.

#SPJ2