Question

When $\dfrac{1}{10}$ percent of 5000 is subtracted from $\dfrac{1}{10}$ of 5000, the difference is,
A. 0
B. 50
C. 450
D. 495
E. 500

Answer 1

Hint: We need to find $\left( ~\dfrac{1}{10}percent\text{ }of\text{ }5000\text{ }-\dfrac{1}{10}~of\text{ }5000 \right)$
We can break this problem into two parts:
(1) Find $\dfrac{1}{10}$ percent of 5000.
(2) Find $\dfrac{1}{10}$ of 5000.
After finding two parts separately, we will subtract the value we get for part 1 from the value we get for part 2. In this way, we will be able to get the required answer.

Complete step-by-step solution -
Let’s start with part 1:
To calculate $\dfrac{1}{10}$ percent of 5000, we must first remember to divide $\dfrac{1}{10}$ by 100.
Since, percent means per 100 (i.e. divided by 100)
So, we have:
$\dfrac{\left( \dfrac{1}{10} \right)}{100}$
To divide a number by 100 means to multiply it by $\left( \dfrac{1}{100} \right)$, so we have;
$\dfrac{1}{10}\times \dfrac{1}{100}=\dfrac{1}{1000}$
Thus, $\dfrac{1}{10}$ percent of 5000
(“of” stands for multiplication)
$\begin{align}
  & =\dfrac{1}{1000}\times 5000 \\
 & =5 \\
\end{align}$
Now, let’s concentrate on part 2, we need to calculate $\dfrac{1}{10}$ of 5000.
To do this, we simply multiply $\dfrac{1}{10}$ of 5000.
(Since “of” stands for multiplication)
$\begin{align}
  & =\dfrac{1}{10}\times 5000 \\
 & =500 \\
\end{align}$
So, the answer to part 1 is 5 and the answer to part 2 is 500.
Therefore, the required difference,
= 500 – 5
= 495
Therefore, the correct option is (D).

Note: If dividing $\dfrac{1}{10}$ by 100 was confusing consider a simpler example, say we were asked for 20% of a number. Well to get 20% as a fraction, we would divide 20 by 100. So, $20%\ \dfrac{20}{100}\ or\ \dfrac{1}{5}$ (in more simplified form).