How to subtract fractional numbers using complements.

Question

I know how $10$'s and $9$'s complements are used, but I don't know how to use complements to subtract two fractional numbers. For example $108.32-26.30$ . How will we solve it using $10$'s and $9$'s complements? thanks

Answer 1

Apply the 9's complement digit-wise.

$0 \leftrightarrow 9$

$1 \leftrightarrow 8$

$2 \leftrightarrow 7$

$3 \leftrightarrow 6$

$4 \leftrightarrow 5$

$108.32 \mathop\to\limits_{9\text{'s complement}} 801.67$

$26.30 \mathop\to\limits_{9\text{'s complement}} 973.69$

The only difference is that when you subtract the repetition of $9$'s, it continues into the decimal like so:

\begin{align}108.32 - 26.30 &= 108.32 + \mathop\sim\limits_9 26.30 - 999.99 \\ &= 108.32 + 973.69 - 999.99 \\ &= 1082.01 - 999.99 \\ &= 82.02 \end{align}