Evaluate the following repeating decimal
4.57
Evaluate the repeated piece
The repeated piece 57 has a length of 2
Therefore, we setup two equations
Equation 1: x = 4.57
Equation 2: 100x = 102 100x 4.57
100x = 100 x 4.57
100x = 457
Subtract equations
Therefore, we have 100x - x = 457.57 - 4.57
99x = 453
Divide each side by 99
| 99x | |
| 99 |
| = |
| 453 |
| 99 |
| x = | 453 |
| 99 |
Simplify using a GCF of 3
| 453/3 | |
| 99/3 |
Final Answer
151/33
