Units and Conversions — Solutions — Grade 11 General Maths

Q1 — Length conversions

Fluency

Key conversions: 1 km = 1000 m; 1 m = 100 cm; 1 cm = 10 mm

(a) 3.5 km to m:

3.5 × 1000 = 3500 m

(b) 450 cm to m:

450 ÷ 100 = 4.5 m

(c) 8200 mm to cm:

8200 ÷ 10 = 820 cm

(d) 0.076 km to cm:

0.076 km × 1000 = 76 m

76 m × 100 = 7600 cm

Q2 — Mass conversions

Fluency

Key conversions: 1 t = 1000 kg; 1 kg = 1000 g; 1 g = 1000 mg

(a) 4.2 kg to g:

4.2 × 1000 = 4200 g

(b) 850 mg to g:

850 ÷ 1000 = 0.85 g

(c) 3500 g to kg:

3500 ÷ 1000 = 3.5 kg

(d) 2.1 t to kg:

2.1 × 1000 = 2100 kg

Q3 — Area conversions

Fluency

Key conversions: 1 m² = 10 000 cm²; 1 km² = 1 000 000 m²; 1 ha = 10 000 m²

(a) 5 m² to cm²:

5 × 10 000 = 50 000 cm²

Reason: Each metre = 100 cm, so 1 m² = 100 × 100 = 10 000 cm²

(b) 85 000 cm² to m²:

85 000 ÷ 10 000 = 8.5 m²

(c) 3.4 km² to m²:

3.4 × 1 000 000 = 3 400 000 m²

Reason: 1 km = 1000 m, so 1 km² = 1000 × 1000 = 1 000 000 m²

(d) 25 000 m² to ha:

25 000 ÷ 10 000 = 2.5 ha

Q4 — Volume and capacity conversions

Fluency

Key conversions: 1 L = 1000 mL; 1 m³ = 1 000 000 cm³; 1 cm³ = 1 mL; 1 m³ = 1000 L = 1 kL

(a) 3 L to mL:

3 × 1000 = 3000 mL

(b) 4500 mL to L:

4500 ÷ 1000 = 4.5 L

(c) 2.5 m³ to cm³:

2.5 × 1 000 000 = 2 500 000 cm³

Reason: 1 m = 100 cm, so 1 m³ = 100³ = 1 000 000 cm³

(d) 6000 cm³ to L:

6000 cm³ = 6000 mL (since 1 cm³ = 1 mL)

6000 ÷ 1000 = 6 L

Q5 — Rectangular garden: area and fertiliser

Understanding

Garden dimensions: 8.5 m × 4.2 m

(a) Area in m²:

A = 8.5 × 4.2 = 35.7 m²

(b) Area in cm²:

35.7 m² × 10 000 = 357 000 cm²

(c) Scoops of fertiliser needed:

Coverage per scoop = 0.5 m²

Scoops needed = 35.7 ÷ 0.5 = 71.4

Round up to whole scoops: 72 scoops

Always round up for coverage problems — 71 scoops would leave part of the garden unfertilised.

Q6 — Storage tank capacity conversions

Understanding

Tank capacity = 12.6 kL

(a) Express in litres:

12.6 kL × 1000 = 12 600 L

(b) Express in millilitres:

12 600 × 1000 = 12 600 000 mL

(c) Express in cubic metres:

1 kL = 1 m³, so 12.6 kL = 12.6 m³

Volume when 3/4 full:

(3/4) × 12 600 L = 9450 L

Q7 — Speed conversions

Understanding

(a) Convert 60 km/h to m/s:

60 km/h means 60 kilometres per hour.

Step 1: Convert km to m: 60 km = 60 000 m

Step 2: Convert h to s: 1 hour = 3600 seconds

Speed = 60 000 m ÷ 3600 s = 16.67 m/s

60 km/h = 16.7 m/s (to 1 d.p.)

General rule: to convert km/h to m/s, divide by 3.6

(b) Convert 15 m/s to km/h:

Step 1: Convert m to km: 15 m = 0.015 km

Step 2: Convert s to h: 1 s = 1/3600 h, so 1 m/s = 3600 m/h = 3.6 km/h

15 × 3.6 = 54 km/h

General rule: to convert m/s to km/h, multiply by 3.6

Q8 — Block of land area in different units

Understanding

Block dimensions: 450 m × 320 m

(a) Area in m²:

A = 450 × 320 = 144 000 m²

(b) Area in hectares:

1 ha = 10 000 m²

144 000 ÷ 10 000 = 14.4 ha

(c) Area in km²:

1 km² = 1 000 000 m²

144 000 ÷ 1 000 000 = 0.144 km²

Q9 — Swimming pool volume and fill time

Problem Solving

Pool dimensions: 25 m × 12 m × 1.8 m deep

(a) Volume in m³:

V = 25 × 12 × 1.8 = 540 m³

(b) Capacity in kL:

1 m³ = 1 kL

Capacity = 540 kL

(c) Time to fill at 80 L/min:

Total volume = 540 kL = 540 000 L

Time = 540 000 ÷ 80 = 6750 minutes

Convert to hours: 6750 ÷ 60 = 112.5 hours

= 112 hours and 30 minutes

It takes 112 hours 30 minutes (4 days 16.5 hours) to fill the pool.

Q10 — Paint required for a room

Problem Solving

Coverage: 12 m² per litre

Room: two walls 5 m × 2.7 m and two walls 3.5 m × 2.7 m

(a) Total area to paint:

Two larger walls: 2 × (5 × 2.7) = 2 × 13.5 = 27 m²

Two smaller walls: 2 × (3.5 × 2.7) = 2 × 9.45 = 18.9 m²

Total area = 27 + 18.9 = 45.9 m²

(b) Litres of paint needed:

Litres = 45.9 ÷ 12 = 3.825 L

Round up: 3.825 L (need to purchase at least this much)

(c) Cost: paint in 4 L tins at $42 each

Tins needed: 3.825 L ÷ 4 L per tin = 0.956 tins

Round up to whole tins: 1 tin needed

Cost = 1 × $42 = $42

One 4 L tin is sufficient since 3.825 L < 4 L.