Number Operations and Properties

A quintal is a unit of mass in the metric system which is equal to $100$ kilograms.

Order of magnitude of $379$ is $\dfrac { 379 }{ { 10 }^{ 2 } } =3.79<{ 5 }^{ -1 }$    i.e, $379\approx { 10 }^{ 2 }$

We have,

$587\times 999=587\times (1000-1)$
$=587\times 1000-587\times 1$
$=587000-587$
$=586413$

$93521\times 625=935421\times {5}^{4}=935421\times {(\cfrac{10}{2})}^{4}$
$\cfrac{935421\times{10}^{4}}{{2}^{4}}=\cfrac{9354210000}{16}$
$=584638125$

$2056\times 987=2056\times (1000-13)$
$=2056\times 1000-2056\times 13$
$=2056000-26728$
$=2029272$.

$72519\times 9999=72519\times(10000-1)$
$=72519\times 10000-72519\times1$
$=725190000-72519$
$=725117481$

$12345679\times 72=123456789\times (70+2)$
$=12345679\times 70+123445679\times 2$
$=864197530+24691358$
$=888888888$

$(112\times {5}^{4})=112\times { \left( \cfrac { 10 }{ 2 }  \right)  }^{ 4 }=\cfrac { 112\times { 10 }^{ 4 } }{ { 2 }^{ 4 } } =\cfrac { 1120000 }{ 16 } =70000$

$5358\times 51=5358\times (50+1)$
$=5358\times 50+5358\times 1$
$=267900+5358$
$=273258$

1397×1397=13972.

12 * 14 = 168. This is a standard multiplication.

32 * 24 = 768. This is calculated using the Urdhva Tiryakbhyam method.