Theory question 101
Fractions, Decimals and Approximation(a) Without using tables or calculator, simplify: (0.6 × 32 × 0.004)/(1.2 × 0.008 × 0.16) leaving the answer in standard form (scientific notation).
(b) In the diagram, EF is parallel to GH. If ∠AEF = 3x°, ∠ABC = 120° and ∠CHG = 7x°, find the value of ∠GHB.
Show the model answer
Model answer
(a) Numerator = 0.0768; denominator = 0.001536. 0.0768 ÷ 0.001536 = 50 = 5.0 × 101.
(b) Through B draw a line parallel to EF and GH. BA makes 3x with it (corresponding to ∠AEF), so BC makes 120° − 3x with it.
∠GHB = 120° − 3x (alternate angles).
B, H, C are on a straight line: (120 − 3x) + 7x = 180 → x = 15.
∠GHB = 120° − 45° = 75°.
Explanation
Draw a line through the bend parallel to the given lines.