# Converting from scientific notation to binary notation.

I am trying to convert 3.984375 * 10^(-1) to binary notation. This is the easiest way I've found but I'm having trouble.

in decimal: $$3.984375*10^{-1} = 0.3984375$$

$$\frac{51}{128} = \frac{110011}{2^7} = 110011 * 2^{-7} = 1.10011 * 2^{-2}$$

How do I go from decimal to fraction easily? That took me a long time.

I have another:

3.4375*10^{-1} = .34375 in decimal.


How do I take this to a fraction?

.34375 x 2 = 0.6875

Thus .34375 in decimal = .01011 in binary.