## Algorithm

Problem Name: 972. Equal Rational Numbers

Given two strings `s` and `t`, each of which represents a non-negative rational number, return `true` if and only if they represent the same number. The strings may use parentheses to denote the repeating part of the rational number.

A rational number can be represented using up to three parts: `<IntegerPart>`, `<NonRepeatingPart>`, and a `<RepeatingPart>`. The number will be represented in one of the following three ways:

• `<IntegerPart>`
• For example, `12`, `0`, and `123`.
• `<IntegerPart><.><NonRepeatingPart>`
• For example, `0.5`, `1.`, `2.12`, and `123.0001`.
• `<IntegerPart><.><NonRepeatingPart><(><RepeatingPart><)>`
• For example, `0.1(6)`, `1.(9)`, `123.00(1212)`.

The repeating portion of a decimal expansion is conventionally denoted within a pair of round brackets. For example:

• `1/6 = 0.16666666... = 0.1(6) = 0.1666(6) = 0.166(66)`.

Example 1:

```Input: s = "0.(52)", t = "0.5(25)"
Output: true
Explanation: Because "0.(52)" represents 0.52525252..., and "0.5(25)" represents 0.52525252525..... , the strings represent the same number.
```

Example 2:

```Input: s = "0.1666(6)", t = "0.166(66)"
Output: true
```

Example 3:

```Input: s = "0.9(9)", t = "1."
Output: true
Explanation: "0.9(9)" represents 0.999999999... repeated forever, which equals 1.  [See this link for an explanation.]
"1." represents the number 1, which is formed correctly: (IntegerPart) = "1" and (NonRepeatingPart) = "".
```

Constraints:

• Each part consists only of digits.
• The `<IntegerPart>` does not have leading zeros (except for the zero itself).
• `1 <= <IntegerPart>.length <= 4`
• `0 <= <NonRepeatingPart>.length <= 4`
• `1 <= <RepeatingPart>.length <= 4`

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const isRationalEqual = function (S, T) {
return f(S) === f(T)
}

function f(S) {
let i = S.indexOf('(')
if (i > 0) {
let base = S.slice(0, i)
let rep = S.slice(i + 1, S.length - 1)
for (let j = 0; j  <  20; ++j) base += rep
return +base
}
return +S
}
``````
Copy The Code &

Input

cmd
s = "0.(52)", t = "0.5(25)"

Output

cmd
true

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def isRationalEqual(self, S, T):
def f(s):
i = s.find('(')
if i >= 0:
s = s[:i] + s[i + 1:-1] * 20
return float(s[:20])
return f(S) == f(T)
``````
Copy The Code &

Input

cmd
s = "0.(52)", t = "0.5(25)"

Output

cmd
true