Decimal fractions have denominators that are powers of 10. Recurring decimals can always be written as ordinary fractions.
1Operations
Multiplication: multiply as whole numbers, then place as many decimals as the factors have in total
Division: shift the decimal point in both numbers until the divisor is a whole number
2Recurring decimals
Pure recurring: 0.ab̄ = ab/99, 0.abc̄ = abc/999
Mixed recurring: 0.ab̄c̄ = (abc − a)/990
3Comparing fractions
Convert to decimals, or cross-multiply: a/b > c/d if ad > bc