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 =