Rational numbers, powers, square roots and repeating decimals

The k-th power of a number n is n^k, the product of k factors equal to n. An even power of a negative number is positive and an odd power is negative: (−2)³ = −8 and (−2)⁴ = 16. The arithmetic square root of a positive number S is the positive number a with a² = S: √S = a. For example √100 = 10, √1.21 = 1.1 and √(25/36) = 5/6. Dividing a common fraction by long division gives a finite or an infinite repeating decimal: 1/3 = 0.(3) and 5/11 = 0.(45). A reduced fraction whose denominator has only the prime factors 2 and 5 becomes a finite decimal. To turn a pure repeating decimal into a common fraction, write the period as the numerator and as many 9s as the period has digits as the denominator: 0.(7) = 7/9 and 0.(45) = 45/99 = 5/11. Infinite non-repeating decimals such as π are not rational.