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(i) Express $5\ cm$ in metre and kilometre.
(ii) Express $35\ mm$ in $cm, m$ and $km$.
To do :
(i) We have to express $5\ cm$ in meter and kilometer.
(ii) We have to express $35\ mm$ in $cm, m$ and $km$.
Solution :
(i) We know that,
$1\ km = 1000\ m$ and $1\ m = 100\ cm$
This implies,
$1\ cm = \frac{1}{100}\ m = 0.01\ m$
$1\ cm = 0.01 \times 1\ m$
$= 0.01 \times \frac{1}{1000} km$
$= 0.01 \times 0.001\ km$
$= 0.00001\ km$
Therefore,
$5\ cm = 5 \times 0.01\ m$
$= 0.05\ m$
$= 5 \times 10^{-2}\ m$.
$5\ cm = 5 \times 0.00001\ km$
$= 0.00005\ km$
$= 5 \times 10^{-5}\ km$.
(ii) We know that,
$10\ mm=1\ cm$
This implies,
$1\ mm=\frac{1}{10}\ cm$
$35\ mm=35\times\frac{1}{10}\ cm$
$35\ mm=3.5\ cm$
Now, converting $3.5\ cm$ to $m$, we get,
$100\ cm=1\ m$
This implies,
$1\ cm=\frac{1}{100}\ m$
Therefore,
$3.5\ cm=3.5\times\frac{1}{100}$
$3.5\ cm=0.035\ m$
Again, converting $0.035\ m$ into $km$
$1000\ m=1\ km$
This implies,
$1\ m=\frac{1}{1000}\ km$
Therefore,
$0.035\ m=0.035\times\frac{1}{1000}\ km$
$0.035\ m=0.000035\ km$