The fraction for the recurring decimal 0.535353 ......... Is
Answers
Answer:
answer is 53/9
Step-by-step explanation:
0.535353...
x=0.535353...
10x=10×0.535353...
10x=53.535353...
Subtracting both the equations
9x=53
x=53/9
answer + 53/9
The fraction for the recurring decimal 0.5353 . . . is equal to 53/99.
Solution: Let this recurring decimal be equal to x.
x = 0.5353 . . . -----equation (i)
Now, we form a new equation on multiplying x with a number such that the repeating digits after the decimal remains the same so that they can be cancelled out on subtracting the two equations.
Clearly, x must be multiplied by 100 to form the new equation.
100x = 53.5353 . . . ---- equation (ii)
Subtracting equation (i) from equation (ii), we get:
100x-x = 53.5353 . . - 0.5353 . .
=> 99 x = 53
=> x = 53/99
The fraction for this recurring decimal is equal to 53/99.