IB Mathematics SL 1.6 Approximation decimal places, significant figures AI HL Paper 2- Exam Style Questions- New Syllabus

(a) (i) 0.030473 rounded to 3 significant figures: First three non-zero digits are 3, 0, 4, with the next digit 7 (≥ 5), so round up: 0.0305 A1.

(ii) 2034999 rounded to 3 significant figures: First three digits are 2, 0, 3, with the next digit 4 (< 5), so no rounding up: 2030000 A1.

(iii) 2.3011 rounded to 3 significant figures: First three digits are 2, 3, 0, with the next digit 1 (< 5), so no rounding up: 2.30 A1.

[2 marks]

(b) Given \( x = 1.3 \times 10^5 = 130000 \) and \( y = 2 \times 10^{-5} = 0.00002 \).

(i) Exact value of \( x + y = 130000 + 0.00002 = 130000.00002 \) A1.

(ii) Compute \( \frac{x}{y} = \frac{1.3 \times 10^5}{2 \times 10^{-5}} = \frac{1.3}{2} \times 10^{5 – (-5)} = 0.65 \times 10^{10} \).

Convert to standard form \( a \times 10^k \), where \( 1 \leq a < 10 \): \( 0.65 \times 10^{10} = 6.5 \times 10^9 \), with \( a = 6.5 \) (correct to 3 significant figures) M1 A1.

[3 marks]

(c) \( A = 2.36 \) to 3 significant figures. The range of possible values is determined by the rounding interval:

Lower bound: \( 2.355 \), upper bound: \( 2.365 \).

Range: \( [2.355, 2.365) \) A2.

[2 marks]