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