Question

What is 1.6 as a fraction?

Answer 1

Hint: Assume the given decimal number as x. Now, count the number of digits present in x after the decimal point. Multiply both the sides with ${{10}^{n}}$ where n is the number of digits counted. Finally, divide both the sides with ${{10}^{n}}$ and to get the required fraction. Cancel the common factors if present to get the simplest form of the obtained fraction.

Complete step by step answer:
Here, we have been provided with the decimal number 1.6 and we are asked to convert it into the fraction. But first we need to remove the decimal point from the number.
Let us assume this number as x, so we have,
$\Rightarrow x=1.6$
Now, as we can see that there is only one digit after the decimal point in 1.6, to remove the decimal point we need to shift this decimal point 1 place to the right which can be done by multiplying it with 10. So, multiplying both the sides with 10 we get,
$\begin{align}
  & \Rightarrow 10x=1.6\times 10 \\
 & \Rightarrow 10x=16 \\
\end{align}$
Now we need to make the coefficient of x equal to 1 so dividing both the sides with 10 we get,
$\Rightarrow x=\dfrac{16}{10}$
Here, we can simplify the expression further by cancelling the common factor 2, so we get,
$\therefore x=\dfrac{8}{5}$

Therefore, the fractional representation of 1.6 is $\dfrac{8}{5}$.

Note: Note that sometimes we will be provided with a non – terminating repeating decimal number whose fractional form will be asked. In such cases we have a different process to get the answer. You must also remember the conversion of fraction into a decimal number. In that case we try to convert the denominator into 10 or a number that can be written in the form ${{10}^{n}}$. Finally we shift the decimal point n digits to the left to get the decimal number.