Express each of the following as a fraction in simplest form.(i) (ii) (iii) (iv) (v) (vi) (vii) (viii)

(i) Given

Let x equals to the repeating decimal =

As we can see the repeating digit is 3

x = 0.3333333……… (i)

10x = 3.333333……… (ii)

Subtracting (i) from (ii), we get

10x - x = 3.3333 – 0.3333

9x = 3

So, we can say that 0.3333333333…. is equals to the .

(i) Given

Let x equals to the repeating decimal =

As we can see the repeating digit is 3

x = 1.3333333……… (i)

10x = 13.333333……… (ii)

Subtracting (i) from (ii), we get

10x-x = 13.3333 – 1.3333

9x = 12

So, we can say that 1.3333333333…. is equals to the

(ii)

Let x equals to the repeating decimal =

As we can see the repeating digit is 34

X = 0.3434343434……… (i)

10x = 3.434343434……… (ii)

100x = 34.3434343434….. (iii)

Subtracting (i) from (iii), we get

100x-x = 0.34343434 – 34.34343434

99x = 34

So, we can say that 0.34343434343434…. is equals to the

(iii)

Let x equals to the repeating decimal =

As we can see the repeating digit is 14

X = 3.1414141414……… (i)

10x = 31.41414141414……… (ii)

100x = 314.1414141414….. (iii)

Subtracting (i) from (iii), we get

100x - x = 3.1414141414 – 314.14141414

99x = 311

So, we can say that 3.1414141414…. is equals to the

(iv)

Let x equals to the repeating decimal =

As we can see the repeating digit is 324

X = 0.324324324324324……… (i)

10x = 3.24324324324324……… (ii)

100x = 32.4324324324324….. (iii)

1000x = 324.324324324324…….(iv)

Subtracting (i) from (iv), we get

1000x - x = 0.324324324324 – 324.324324324324

999x = 324

So, we can say that 0.324324324324324324324…. is equals to the

(v)

Let x equals to the repeating decimal =

As we can see the repeating digit is 7

x = 0.17777777777……… (i)

10x = 1.777777777……… (ii)

100x = 17.77777777….. (iii)

Subtracting (ii) from (iii), we get

100x - 10x = 17.777777-1.777777

90x = 16

So, we can say that 0.17777777…. is equals to the

(vi)

Let x equals to the repeating decimal =

As we can see the repeating digit is 4

X = 0.5444444444……… (i)

10x = 5.44444444……… (ii)

100x = 54.444444….. (iii)

Subtracting (ii) from (iii), we get

100x-10x = 54.44444-5.44444

90x = 49

So, we can say that 0.5444444…. is equals to the

(vii)

Let x equals to the repeating decimal =

As we can see the repeating digit is 63

X = 0.16363636363……… (i)

10x =1.6363636363……… (ii)

100x = 16.363636363….. (iii)

1000x = 163.63636363…. (iv)

Subtracting (ii) from (iv), we get

1000x-10x = 163.636363-1.63636363

990x = 162

So, we can say that 0.16363636363…. is equals to the

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