Express each of the following as a fraction 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 1/3.


(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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