2. A Solution

The method that the original developers finally hit upon uses the idea of scientific notation. Scientific notation is a standard way to express numbers; it makes them easy to read and compare. You're probably familiar with scientific notation with base-10 numbers. You just factor your number into two parts: a value in the range of [1 <= n < 10], and a power of 10. For example:

3498523 is written as 3.498523 * 10⁶
-0.0432 is written as -4.32 * 10^-2

The same idea applies here, except that you need to use powers of 2 because the computer deals with binary numbers. Just factor your number into a value in the range [1 <= n < 2], and a power of 2. ^*

-6.84 is written as -1.71 * 2²
0.05 is written as 1.6 * 2^-5

I factored my number - now let's make a bitstring! ->