Question

The decimal representation of $\dfrac{93}{1500}$ will be
a) Terminating
b) Non-terminating
c) Non-terminating, repeating
d) Non-terminating, non-repeating

Answer 1

Hint: Terminating a number means ending that number after the decimal or it will have fixed digits. Recurring means repetitive, i.e. digits are getting repeated. And non-terminating and non-recurring are just vice-versa of terminating and recurring. Use this definition and divide the given fraction in decimal form and observe the property of that number from the options provided.

Complete Step-by-Step solution:
Terminating decimals: these have a finite number of digits after the decimal points.
Example: 0.12, 0.1355, 6.88 etc.
Recurring decimals: these have one or more repeating numbers or sequence of numbers after the decimal point, which continue to infinity.
Example: 0.5555…….., 2.343434…………… etc.
Decimals which go on forever, never ending termed as non-terminating and decimals which go on forever, never ending and never forming a repeating pattern is termed as non-recurring. Example: 1.10123143202……….
So, we need to divide 93 by 1500 as per the given fraction. As per the given fraction, we can observe that 93 and 1500, both will be divisible by 3. So, let us just simplify the given fraction by dividing 93 and 1500 by 3. So, we get
$\dfrac{93}{1500}=\dfrac{31}{500}$
Now, divide31 by 500 in decimal form to get the correct answer. So, let us divide 31 by 500. So, we get
$500\overset{0.062}{\overline{\left){\begin{align}
  & 3100 \\
 & \underline{3000} \\
 & 1000 \\
 & \underline{1000} \\
 & 0000 \\
\end{align}}\right.}}$
Hence, on dividing 31 by 500 we get 0.062. As 0.062 is the terminating form of decimal, so we get the decimal representation of $\dfrac{93}{1500}$ as terminating one. Hence, option (a) is correct.

Note: One may divide 93 by 1500 directly as well without converting to simplified fraction. 1500 is a large number so it can be complex to solve that division. So, we can simplify the fraction first, then try to divide. One may get the same answer if he/she divides 93 by 1500 as well, so apply any approach.
Take care with the division part as 31 is less than 500, so, we need to put decimal in the quotient then we can proceed further. So, be careful with this part as well.