Question

Express 'mile', in terms of kilometre. (1 mile $=$ 1.760 yards, 1 yard $=$ 36 inches and 1 inches $=$ 2.54 cm).
[Note : Mile, yard and inch are practical units of length].

Answer 1

To find, 1 mile $=\stackrel{?}{..........}$ kilometre (km)
Given,
1 mile $=$ 1.760 yards
and 1 yard $=$ 36 inches
$\therefore$ 1 mile $1.760\times 36inches$
$1mile=1.760\times 36\times 2.54cm$
$(1inch=2.54cm)$
$\therefore$ 1mile $1.760\times 36\times 2.54\times {10}^{-2}metre$ ......... (1)
$1km={10}^{3}metre$ ............ (2)
Dividing (1) by (2) we get
$\Rightarrow \frac{1mile}{1km}$
$=\frac{1.760\times 36\times 2.54\times {10}^{-2}metre}{{10}^{3}metre}$
$\Rightarrow 1mile=1.760\times 36\times 2.54\times {10}^{-5}km$
$\Rightarrow 1mile=1.6093\times {10}^{-3}km$