Question

How do you write $\dfrac{63}{40}$ as a decimal ?

Answer 1

Hint: For these kinds of questions, all we need is basic mathematics. We just have to divide and express them in decimals. Now , the number of digits after the decimal is our wish unless it is clearly specified in the question. We generally limit it 2 or 3. But the number of digits after the decimal point to be written also depends upon the type of decimal it is.

Complete step by step answer:
There are in general 2 types of decimals.
They are terminating and non - terminating. From the name itself , we can guess that decimals which culminate after a certain digit are called terminating decimals. For example : $\dfrac{2}{10}=0.2,\dfrac{5}{2}=2.5$ etc. No matter the number of digits after the decimal point , if they end or terminate at one point , then they are terminating decimals.
Non – terminating decimals are those which do not end. The number of digits after the decimal point keeps going. There are two kinds of non – terminating decimals. They are repeating non – terminating decimals and non – repeating non – terminating decimal points.
Repeating non – terminating decimals are those which follow a certain pattern in the digits after the decimal point. There is a particular trend which you can see. For example : $2.314314314.....$ we can see a pattern $.314$ . So we can just stop after $2.314$.
Non – repeating non – terminating decimals are those which do not terminate and they also don’t have a significant pattern. The famous example of non – repeating non – terminating decimal is the value of $\pi $ . The value of $\pi $ is 3.1415926….. and it just never ends.
So now let us divide $\dfrac{63}{40}$ .
Upon dividing it, we get the following :
\[\Rightarrow \dfrac{63}{40}=1.575\]
Now this is terminating decimal.
$\therefore \dfrac{63}{40}=1.575$ .

Note: In most questions , we do leave the fraction as it is . But it is mentioned then we have to proceed to further calculation. And all the values of $\sqrt{2},\sqrt{3},\sqrt{5}....$ etc are all non – repeating non – terminating decimals. All these are supposed to be left as the radical expressions they are. Just be careful while dividing and check with the question to see how many digits are to be present after the decimal point. Sometimes we also just round off the digits after the decimal point.