Converting from scientific notation to binary notation.

Question

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?

Answer 1

Aren't you allowed to convert the mantissa(fractional part) directly into binary?

If you are allowed, then multiply by 2 at each step and remember the integer part:

.34375 x 2 = 0.6875  
0.6875 x 2 = 1.375
0.375 x 2  = 0.75
0.75 x 2 = 1.5
0.5 x 2 = 1.0

Thus .34375 in decimal = .01011 in binary.