Question

Convert the following into fraction in their lowest terms: 0.65

Answer 1

Hint: We will first convert our given decimal quantity into a fraction. For converting decimal to fraction, remember that every place after the decimal point is taken as ${\displaystyle \frac{1}{10}}$. If there is one place after the decimal point, it is taken as ${\displaystyle \frac{1}{10}}$. If there are two places after the decimal then ${\displaystyle \frac{1}{100}}$, if three places then ${\displaystyle \frac{1}{1000}}$ and so on as we move ahead. We will use this to convert the decimal into its fractional form and then simplify it to get it in its lowest terms.

Complete step-by-step answer:
Let us first convert the decimal into its fractional form. The decimal number given to us is equal to 0.65, that is, there are exactly two digits after the decimal point. So, in order to convert the given decimal quantity into a fraction, we will divide it by hundred. This can be done as follows:
Let the fractional form of 0.65 be ‘x’. Then ‘x’ can be calculated as follows:
$\Rightarrow x={\displaystyle \frac{65}{100}}$
Now that we have our number in its fractional form, we can simply convert it into its lowest terms by cancelling out common factors from numerator and denominator. This can be done as follows:
$\begin{array}{rl}& \Rightarrow x={\displaystyle \frac{65}{100}}\\ & \Rightarrow x={\displaystyle \frac{13\times 5}{20\times 5}}\\ & \therefore x={\displaystyle \frac{13}{20}}\end{array}$
Hence, 0.65 when converted into a fraction in lowest terms comes out to be ${\displaystyle \frac{13}{20}}$. This is a proper fraction.

Note: To understand what kind of fraction is formed or given to us, we need to know all the three types of fraction. Firstly, proper fraction is a fraction whose numerator is less than its denominator and in an improper fraction, the condition is reversed. Lastly, in mixed fraction, the whole number is written separately in the left with the proper fraction in the right.