Theory question 101
Fractions, Decimals and Approximation(a) Simplify, without using tables or calculator: ¾(3⅜ + 1⅝)/(2⅛ − 1½)
(b) Given that log102 = 0.3010 and log103 = 0.4771, evaluate correct to 2 significant figures and without using tables or calculator, log101.125.
Show the model answer
Model answer
(a) 3⅜ + 1⅝ = 5, so the numerator is ¾ × 5 = 15/4. Denominator: 17/8 − 12/8 = 5/8.
15/4 ÷ 5/8 = 15/4 × 8/5 = 6.
(b) 1.125 = 9/8 = 32/23.
log 1.125 = 2(0.4771) − 3(0.3010) = 0.9542 − 0.9030 = 0.0512 ≈ 0.051.
Explanation
Write 1.125 as a fraction made of powers of 2 and 3.