You seem to misunderstand what a 'base" means; as with all numbers in common usage in Western society, the number $1,048,576$ is in base 10. For reference, here is the relevant Wikipedia page. Remember that in "base $b$" notation, the string of digits $(a_n\ldots a_1a_0)$ denotes
$$a_nb^n+\cdots+a_1b+a_0$$
so for example, $10,048,576$ denotes
$$(1\times 10^7)+(0\times 10^6)+(0\times 10^5)+(4\times 10^4)+(8\times 10^3)+(5\times 10^2)+(7\times 10^1)+(6\times 10^0)$$
However, in base 2, the same number would be written $$1\underbrace{0000000000000000000}_{19\text{ zeros}}=(1\times 2^{20})+(0\times 2^{19})+\cdots+(0\times 2^0)$$
Now on to how to convert. Because
$$1\text{ megabit}=1,000,000\text{ bits},\quad 1\text{ mebibit}=1,048,576\text{ bits}$$
if you have $1.048576$ megabits, you have
$$1.048576\times (1\text{ megabit})=1.048576\times 1,000,000\text{ bits}=1,048,576\text{ bits}=1\text{ mebibit}.$$
If you have $\frac{1}{1.048576}$ mebibits, you have
$$\frac{1}{1.048576}\times(1\text{ mebibits})=\frac{1}{1.048576}\times 1,048,576\text{ bits}$$ $$=\frac{1}{1.048576}\times1.048576\times 1,000,000\text{ bits}=1,000,000\text{ bits}=1\text{ megabit}$$
Thus, $1$ megabit equals $\frac{1}{1.048576}$ mebibits, and 1 mebibit equals $1.048576$ megabits, and to convert any other number of megabits or mebibits, just multiply:
$$x\text{ megabits}=\frac{x}{1.048576}\text{ mebibits}$$
and
$$y\text{ mebibits}=(1.048576\times y)\text{ megabits}.$$
In even more generality, if one "blah" equals $X$ "foos" and one "kwip" equals $Y$ "foos", then one blah equals $\frac{X}{Y}$ kwips and one kwip equals $\frac{Y}{X}$ blahs.