This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Exercise 4: Classify as rational or irrational Step 1: 0.53 This is a terminating decimal. 0.53 = (53)/(100) Terminating decimals are rational. Rational Step 2: 0.218 This is a terminating decimal. 0.218 = (218)/(1000) = (109)/(500) Rational Step 3: 0.396 This is a terminating decimal. 0.396 = (396)/(1000) = (99)/(250) Rational Step 4: 0.52 This is a repeating decimal. Let x = 0.52. 100x = 52.52 100x - x = 52.52 - 0.52 99x = 52 x = (52)/(99) Repeating decimals are rational. Rational Exercise 5: Convert repeating decimals to fractions Step 1: 0.16 Let x = 0.16. 100x = 16.16 100x - x = 16 99x = 16 x = (16)/(99) (16)/(99) Step 2: 0.6 Let x = 0.6. 10x = 6.6 10x - x = 6 9x = 6 x = (6)/(9) = (2)/(3). (2)/(3) Step 3: 0.25 Let x = 0.25. 100x = 25.25 100x - x = 25 99x = 25 x = (25)/(99). (25)/(99) Step 4: 0.46 Let x = 0.46. 100x = 46.46 100x - x = 46 99x = 46 x = (46)/(99). (46)/(99)