# Converting numbers (binary and so on)

1. Apr 5, 2009

### soonsoon88

Anyone can help me to solve the problem?

how to convert 0.65 (decimal numbers) to binary,octal and hexadecimal numbers?
thx..=)

2. Apr 5, 2009

3. Apr 5, 2009

### OmCheeto

I would first convert 0.65 into a proper fraction of the lowest common denominator in base 10, convert the numerator and denominator to the new base, then do long division.

0.65 = 65/100 = 13/20 ----> 1101/101002 = 15/248 = D/1416

Of course, you have to know how to do long division in the different bases.

4. Apr 8, 2009

### DoctorBinary

After you've converted 0.65 to binary, there's a shortcut to convert it to octal and hex. Just group the bits into 3s (for octal) and 4s (for hex). For example, 0.101 would be 0.5 in octal and 0.A in hex.

By the way, you can also check your binary answer with the decimal/binary converter I wrote: http://www.exploringbinary.com/binary-converter/ . It is arbitrary precision, which means you can convert very large and very small numbers.

5. Apr 8, 2009

### DoctorBinary

That would be the best way to do it in a computer, but I'd say the "repeated multiplication by new base" method works best for humans!