Express each of the following as a fraction in simplest form.

i. ii.


iii. iv.


v. vi.

i) Let x = 0. - (i)


Multiply 10 on both sides -


10x = 8. - (ii)


Subtract the equations (i) from (ii) -


9x = 8


So x =


ii) Let x = 2. - (i)


Multiply 10 on both sides -


10x = 24. - (ii)


Subtract the equations (i) from (ii) -


9x = 22


So x =


iii) Let x = 0. - (i)


Multiply 100 on both sides -


100x = 24. - (ii)


Subtract the equations (i) from (ii) -


99x = 24


So x = =


iv) Let x = 0.1 - (i)


Multiply 10 on both sides -


10x = 1. - (ii)


Multiply 10 on both sides -


100x = 12. - (iii)


Subtract the equations (ii) from (iii) -


90x = 11


So x =


v) Let x = 2.2 - (i)


Multiply 10 on both sides -


10x = 22. - (ii)


Multiply 10 on both sides -


100x = 224. - (iii)


Subtract the equations (ii) from (iii) -


90x = 202


So x = =


vi) Let x = 0. - (i)


Multiply 1000 on both sides -


1000x = 365. - (ii)


Subtract the equations (i) from (ii) -


999x = 364


So x =


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