Decimal Fraction

$$ = \frac{{3.157 \times 4126 \times 3.198}}{{63.972 \times 2835.121}}$$
$$ \approx \frac{{3.2 \times 4126 \times 3.2}}{{64 \times 2835}}$$
$$ = \frac{{32 \times 4126 \times 32}}{{64 \times 2835}} \times \frac{1}{{100}}$$
$$ = \frac{{66016}}{{2835}} \times \frac{1}{{100}}$$
$$ = \frac{{23.28}}{{100}}$$
$$ = 0.23$$
$$ \approx 0.2$$

477 × 124 × 86 = 5086728
Sum of decimal place = 3
∴ 47.7 × 12.4 × 8.6 = 5086.728

Given, 168 × 32 = 5376 or 5376 ÷ 168 = 32
Now,
$$ = \frac{{5.376}}{{16.8}}$$
$$ = \frac{{53.76}}{{168}}$$
$$ = \left( {\frac{{5376}}{{168}} \times \frac{1}{{100}}} \right)$$
$$ = \frac{{32}}{{100}}$$
$$ = 0.32$$

Converting each of the given fractions into decimal form, we get :
$$\frac{2}{3}$$ = 0.66
$$\frac{3}{5}$$ = 0.6
$$\frac{7}{9}$$ = 0.77
$$\frac{9}{11}$$ = 0.81
$$\frac{8}{9}$$ = 0.88
Clearly, 0.6 < 0.66 < 0.77 < 0.81 < 0.88
So, $$\frac{3}{5}$$ < $$\frac{2}{3}$$ < $$\frac{7}{9}$$ < $$\frac{9}{11}$$ < $$\frac{8}{9}$$

Given expression :
$$ = \frac{{{{\left( {0.1} \right)}^3} + {{\left( {0.02} \right)}^3}}}{{{2^3}\left[ {{{\left( {0.1} \right)}^3} + {{\left( {0.02} \right)}^3}} \right]}}$$
$$ = \frac{1}{8}$$
$$ = 0.125$$

$$\frac{3}{4} = 0.75,\  $$
$$\frac{5}{6} = 0.833,\  $$
$$\frac{1}{2} = 0.5,$$
$$\frac{2}{3} = 0.66,$$
$$\  \frac{4}{5} = 0.8,$$
$$\frac{9}{{10}} = 0.9$$
Clearly, 0.8 lies between 0.75 and 0.833
$$\therefore \frac{4}{5}{\text{lies between}}\frac{3}{4}{\text{and}}\frac{5}{6}$$

$$0.125125... = 0.\overline {125} = \frac{{125}}{{999}}$$

$$617.00$$
$$\,\,\,\,\,\,\,6.017$$
$$\,\,\,\,\,\,\,0.617$$
$$ + \,\,\,6.0017$$
$$ - - - - - - $$
$$\,\,\,629.6357$$
$$ - - - - - - $$

$$\frac{{489.1375 \times 0.0483 \times 1.956}}{{0.0873 \times 92.581 \times 99.749}} \approx \frac{{489 \times 0.05 \times 2}}{{0.09 \times 93 \times 100}}$$
$$ = \frac{{489}}{{9 \times 93 \times 10}}$$
$$ = \frac{{163}}{{279}} \times \frac{1}{{10}}$$
$$ = \frac{{0.58}}{{10}}$$
$$ = 0.058 \approx 0.06$$

2×5 = 10.
Sum of decimal places = 4
∴ 0.002×0.5 = 0.001