Question

What’s a terminating decimal?

Answer 1

Hint: A given decimal number can be classified as either terminating or non-terminating by looking at the numbers after the decimal point. If the numbers keep repeating in a never ending sequence, then we can say that it is a non-terminating decimal. Else, if the decimal point stops at a point and has zeroes after that consistently, we can say that it is a terminating decimal.

Complete step-by-step solution:
Decimal numbers are those which are not integers and have some non-zero value after the decimal point. We get decimal numbers by evaluating fractions which cannot be further simplified, or in other words by rational numbers excluding integers.
Let us assume a fractional number, say $\dfrac{4}{3}$ . Now, you can evaluate this by using long division manually or by plugging in this value into your calculator. This value turns out to be $1.3333333333333$ …….and so on. Clearly we can see that the 3s after the decimal point keep going on and on and do not stop. Hence we can conclude that the given decimal is non-terminating.
Next, let us assume another fractional number, say $\dfrac{8}{5}$. Again, this can be evaluated by either long division manually, or by using a calculator. This value turns out to be $1.6000$ …..and so on. Clearly we can see that after 6 there are zeroes consistently, hence, this is a terminating decimal. All decimal numbers which satisfy this criteria can be classified under terminating decimals.

Note: Any irrational number, say $\pi $ or the Euler’s number $e$ , are non-terminating decimals because the numbers after the decimal point are never ending for such numbers and they go up to infinity.
$\begin{align}
  & \pi =3.14159... \\
 & \,e=2.718.... \\
\end{align}$
 If and only if there are continuous zeroes at some point in the decimal part up to infinity, then the decimal can be called as a terminating one.