IB Mathematics SL 1.6 Approximation decimal places, significant figures AI SL Paper 1- Exam Style Questions- New Syllabus

(a)
Evaluate: \( 6 + \dfrac{13}{16} = \dfrac{96}{16} + \dfrac{13}{16} = \dfrac{109}{16} \). M1
Then: \( \dfrac{1}{\dfrac{109}{16}} = \dfrac{16}{109} \), so \( 3 + \dfrac{16}{109} = \dfrac{327 + 16}{109} = \dfrac{343}{109} \approx 3.14678899 \).
Rounded to four decimal places: 3.1468. A1
[2 marks]

(b)
Approximation: 3.1468. Exact \( \pi \approx 3.1415926535 \).
Absolute error: \( |3.1468 – 3.1415926535| \approx 0.0052073465 \). M1
Percentage error: \( \dfrac{0.0052073465}{3.1415926535} \times 100 \approx 0.165754\% \approx 0.166\% \). A1
[2 marks]