Find a fraction equivalent to the recurring decimal
0.435643564356....
4356/9999
= 484/1111
To find a fraction equivalent to the recurring decimal 0.435643564356..., we can use the concept of geometric series.
Step 1: Let's denote the given recurring decimal as "x":
x = 0.435643564356...
Step 2: Determine the numerator of the fraction.
We need to find a number that contains all the recurring digits without the non-recurring part. In this case, the recurring part is "4356".
Let's multiply x by a power of 10, which ensures that the recurring part ends just before the decimal point. In this case, "4356" will be the entire part of the recurring part.
10000x = 4356.435643564356...
Subtracting the original equation from this equation eliminates the non-recurring part:
10000x - x = 4356.435643564356... - 0.435643564356...
9999x = 4356
Thus, we have determined the numerator of the fraction as 4356.
Step 3: Determine the denominator of the fraction.
To find the denominator, count the number of repeating digits, which is the length of the recurring part. In this case, the recurring part is "4356", which has a length of 4.
Take as many 9s as the length of the recurring part as the denominator.
Therefore, the denominator is 9999.
Step 4: Simplify the fraction (if required).
In this case, the fraction 4356/9999 cannot be simplified further.
Therefore, a fraction equivalent to the recurring decimal 0.435643564356... is 4356/9999.