Theory question 101
Fractions, Decimals and Approximation(a) Simplify: (½ of ¼ ÷ ⅓)/(⅙ − ¾ + ½).
(b) Given that √x = 101̄.6741, without using calculators, find the value of x.
Show the model answer
Model answer
(a) Numerator: ½ × ¼ = 1/8; 1/8 ÷ 1/3 = 3/8.
Denominator: (2 − 9 + 6)/12 = −1/12.
3/8 ÷ (−1/12) = 3/8 × (−12) = −9/2 = −4½.
(b) log √x = 1̄.6741, so ½ log x = 1̄.6741 and log x = 2 × 1̄.6741 = 1̄.3482.
x = antilog 1̄.3482 = 0.2229.
Explanation
'of' means multiply; do it before the division.