Theory question 101
Fractions, Decimals and Approximation(a) Evaluate and express your answer in standard form; (4.56 × 3.6)/0.12
(b) Without using mathematical tables or calculator, evaluate (73.8)2 − (26.2)2
(c) Simplify √(1 19/81), expressing your answer in the form a/b where a and b are positive integers.
Show the model answer
Model answer
(a) (4.56 × 3.6)/0.12 = 4.56 × 30 = 136.8 = 1.368 × 102.
(b) Difference of two squares: (73.8 − 26.2)(73.8 + 26.2) = 47.6 × 100 = 4760.
(c) 1 19/81 = 100/81, so √(100/81) = 10/9.
Explanation
Spot the difference of two squares: a² − b² = (a − b)(a + b).