```ts
/**
 * A divided by b, rounded to 2 decimal places if necessary.
 */
export function safeDivide(a: number, b: number): number {
  if (b === 0 || !Number.isFinite(a) || !Number.isFinite(b)) {
    throw new Error('Both arguments must be finite numbers and non-zero.');
  }
  return parseFloat((a / b).toFixed(2));
}
```