In the following physical units, how many units are there in 1 metre?
(i) 1 Astronomical unit (AU`=1.496xx10^(11)m`
(ii) 1 light year `=9.467xx10^(15)m`
(iii) 1 micron `(mu)=10^(-6)m`
(iv) 1 parallacti second (parsec)
`=3.08xx10^(16)m`
Given data:
`1Au=1.496xx10^(11)m`
`11y=9.467xx10^(15)m`
`1mm=10^(-6)m`
1 parsec `=3.08xx10^(16)m`

Explanation

(i)`1.496xx10^(11)m` is equivalent 1 AU.
1 metre is equivalent to `1/(1.496xx10^(11))`
`=0.6684xx10^(-11)=6.68xx10^(-12)AU`
In one mere `6.68xx10^(-12)` astronomial units are present.
(ii) `9.467xx10^(15)` m is equivalent to 11y.
1 metre is equivalent to `1/(9.467xx10^(15))`
`=0.1056xx10^(-15)=1.05xx10^(-16)ly`
In one mertre., `1.05xx10^(-16)` light years are present.
(iii) `10^(-6)` m equivalent of `1mum`
1 metre is equivalent to `1/(10^(-6))=10^(6)mum`
In one metre `10^(6)` microns are present.
(iv) `3.08xx10^(16)` m equivalent to 1 parsec.
1 matre is equivalent to `1/(3.08xx10^(16))`
`=0.324xx10^(-16)=3.24xx10^(-17)m`
In one metre `3.24xx10^(-17)` parsec are present.