Evaluate the following:

(i) 31.42 - 17.853 - 6.43

(ii) 13.01 - 5.428 - 3.703 + 2.99

(i) Writing each of the given numbers with three decimal places, we get:

Given expression = 31.420 - 17.853 - 6.430

$\phantom{Given expression}$ = 31.420 - (17.853 + 6.430)

Now,

$\begin{array}{r} \phantom{+}17.853 \ +\space 6.430 \ \hline 24.283 \end{array}$

So,

$\begin{array}{r} \phantom{+}31.420 \ -\space 24.283 \ \hline 7.137 \end{array}$

Therefore, 31.42 - 17.853 - 6.43 = 7.137.

(ii) Writing each of the given numbers with three decimal places, we get:

Given expression = 13.010 - 5.428 - 3.703 + 2.990

$\phantom{Given expression}$ = (13.010 + 2.990) - (5.428 + 3.703)

Now,

$\begin{array}{r} \phantom{+}13.010 \ +\space 2.990 \ \hline 16.000 \end{array} \qquad \text{and} \qquad \begin{array}{r} \phantom{+}5.428 \ +\space 3.703 \ \hline 9.131 \end{array}$

So,

$\begin{array}{r} \phantom{+}16.000 \ -\space 9.131 \ \hline 6.869 \end{array}$

Therefore, 13.01 - 5.428 - 3.703 + 2.99 = 6.869.