how to convert decimal 49.25 to hexadecimal?

Question

please explain step by step procedure on how to convert 49.25 to hexadecimal. I don't understand how to convert the decimal part.

Answer 1

First ask yourself $16^k \le 49.25 < 16^{k+1}$ for what power of $k$.

The answer is $16^1 \le 49.25 < 16^2$.

Then ask yourself $49.25 = n*16^1 + r$ for what integer $n; 0\le n < 16$ and for what value of $r; 0\le r < 16$.

The answer is $49.25 = 3*16^1 + 1.25$.

That was to get the digit for the $16^1$ place. Now we need to get the digit for the $16^0 = 1$ place.

So ask yourself $1.25 = n*1 + r$ for what integer $n; 0 \le n < 16$ and for what value of $r; 0\le r < 1$.

The answer is $1.25 = 1*1 + 0.25$.

Now we need to get the digit for the $16^{-1} = \frac 1{16}$ place.

So ask yourself $0.25 = n*\frac 1{16} + r$ for what integer $n; 0 \le n < 16$ and for what value of $r; 0 \le r < \frac 1{16}$.

The answer to that if $0.25 = \frac 14 = 4*\frac 1{16} + 0$.

We got to $0$ and now we stop.

Put it all together and you have found that:

$49.25 = 3*16^1 + 1*16^0 + 4*16^{-1}$.

The hexidecimal notation for this is $49.25 = 31.4_{16}$.

Note: This is equivalent to noting that $49 \frac 14= 4*10^1 + 9*10^0 + 2*10^{-1} + 5*10^{-2}$ so we say $49\frac 14 = 49.25_{10}$.

the only differences are we did our calculations based on $10$ and not $16$, and that somebody told as that FORTY-NINE has a meaning and we should know what it means just be looking at it.