Intuition: Difference in price elasticities of demand due to different bases
The solution to this issue is called "Arc Elasticity", used for "large" absolute changes. On the surface, the formula for Arc Elasticity is the familiar one, for example for price elasticity of demand

$$\eta_{arc}= \dfrac{ \text{
Percentage change in quantity demanded }} {  \text{ Percentage change in price } }$$

But the thing is how these percentage changes are calculated: If we went from quantity $q_a$ to quantity $q_b$, then while we "usually" calculate the percentage change as $(q_b-q_a)/q_a$ for the Arc Elasticity we divide by the mid-point of the interval -not by the point we started with. Same for price. So

$$\eta_{arc}= \dfrac{ \text{
Percentage change in quantity demanded }} {  \text{ Percentage change in price } } = \frac {\frac {q_b-q_a}{(q_b+q_a)/2}}{\frac {p_b-p_a}{(p_b+p_a)/2}}$$

$$\implies \eta_{arc} = \frac {q_b-q_a}{p_b-p_a}\cdot \frac{p_b+p_a}{q_b+q_a}$$

Re-arrange the terms at will to suit your own mnemonic triggers.

The Arc Elasticity has the convenient properties

(1) it is symmetric with respect to the two prices and quantities,
(2) it is independent of the units of measurement,
(3) it yields a value of unity if the total revenues (price times quantity) at the two points are equal. 

See Allen (1933).

P.S. to OP: Use this for your other question.