1. **Matching lengths of objects (A to E) with cards (i to v):** - Given lengths in metres for A to E: - A Dust mite: $0.0002$ m - B Bacterium: $0.000002$ m - C Virus: $0.0000001$ m - D Animal cell: $0.00002$ m - E Plant cell: $0.0001$ m - Given lengths in nm or μm for i to v: - i: $100$ nm - ii: $20$ μm - iii: $200$ μm - iv: $100$ μm - v: $2$ μm 2. **Convert all lengths to the same unit for comparison:** - Recall: - $1$ m $= 10^9$ nm - $1$ m $= 10^6$ μm - Convert A to E from metres to micrometres ($ ext{μm}$): - A: $0.0002$ m $= 0.0002 imes 10^6 = 200$ μm - B: $0.000002$ m $= 0.000002 imes 10^6 = 2$ μm - C: $0.0000001$ m $= 0.0000001 imes 10^6 = 0.1$ μm - D: $0.00002$ m $= 0.00002 imes 10^6 = 20$ μm - E: $0.0001$ m $= 0.0001 imes 10^6 = 100$ μm - Convert i to v to micrometres: - i: $100$ nm $= rac{100}{1000} = 0.1$ μm - ii: $20$ μm (already in μm) - iii: $200$ μm - iv: $100$ μm - v: $2$ μm 3. **Match cards based on equal lengths:** - A (200 μm) matches iii (200 μm) - B (2 μm) matches v (2 μm) - C (0.1 μm) matches i (0.1 μm) - D (20 μm) matches ii (20 μm) - E (100 μm) matches iv (100 μm) --- 4. **Erin's photos storage problem:** - Erin's photo size: $3.6$ MB - Memory card size: $1$ GB - Convert $1$ GB to MB: - $1$ GB $= 1000$ MB (assuming decimal system) - Number of photos Erin can store: $$\text{Number} = \frac{1000}{3.6} \approx 277.78$$ - Erin can store approximately $277$ photos. --- 5. **Sue's photo size suggestion:** - Memory card size: $32$ GB $= 32000$ MB - Number of photos desired: $13000$ - Photo size suggested: $$\text{Photo size} = \frac{32000}{13000} \approx 2.46 \text{ MB}$$ - Suggest Sue uses photos of about $2.5$ MB or smaller to store $13000$ photos. --- **Final answers:** - Matching cards: A-iii, B-v, C-i, D-ii, E-iv - Erin can store about $277$ photos on $1$ GB - Sue should use photos about $2.5$ MB in size