# how to convert decimal 49.25 to hexadecimal?

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

• Hint: $.25_{10} = \frac{1}{4}$. What is a quarter of $16$? – JMoravitz Jun 1 at 15:16
• How about you multiply by $16$, convert to hexadecimal then shift the digits to the right once to get the original number – Peter Foreman Jun 1 at 15:24
• To right number $N$ in hexidecimal you solve $N = a*256 + b*16 + c*1 + d*\frac 1{16} + e*\frac 1{256} + .....$. It's easy to see that $49 = 3*16+1$ so $49_{10}=31_{16}$. But now you need to figure out what $0.25_{10} = d*\frac 1{16} + e*\frac 1{256} + ....$. And we now $0.25 = \frac 14$ and so $\frac 14 = \frac ?{16}$. – fleablood Jun 1 at 15:40
• @JMoravitz don't you mean: How many $16$ths are one quarter?.... oh wait. I guess I see what you meant. – fleablood Jun 1 at 15:41
• Oh, wait... I guess I see what you meant. – fleablood Jun 1 at 15:42

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.