Is there any easy way to estimate this formula?

Question

I often see this formula, the percentage is same,

$$ \frac{28311}{1+16.8\%} \times 16.8\% $$

$$ \frac{21011}{1+15.7\%} \times 15.7\% $$

$$ \frac{11019}{1+12.5\%} \times 12.5\% $$

is there any easy way to estimate the formula?

such as this example,

$$ ( 1+2\% )^{4} \approx 1+2\% \times 4 $$

Answer 1

Using the formula for an infinite geometric series:

$$\frac{1}{1 - (-x)} = 1 -x+x^2 - x^3 + \cdots$$

and hence

$$\frac{x}{1+x} = x - x^2 + x^3 - x^4 + \cdots$$

as long as $|x| < 1$.