IB MYP 4-5 Maths- Metric conversions- Study Notes - New Syllabus
IB MYP 4-5 Maths- Metric conversions – Study Notes
Standard
- Metric conversions
IB MYP 4-5 Maths- Metric conversions – Study Notes – All topics
Metric conversions
Metric Conversions
The metric system is a decimal-based system used worldwide. Converting between metric units involves multiplying or dividing by powers of 10.
1. Key Idea
Moving to the right in the metric table (smaller units) → multiply by 10.
Moving to the left (larger units) → divide by 10.
2. Common Metric Prefixes
| Prefix | Symbol | Value |
|---|---|---|
| kilo | k | 1,000 |
| hecto | h | 100 |
| deca | da | 10 |
| base unit | m, g, L | 1 |
| deci | d | 0.1 |
| centi | c | 0.01 |
| milli | m | 0.001 |
3. Standard Metric Units
- Length: mm, cm, m, km
- Mass: mg, g, kg, tonne
- Capacity: mL, L, kL
4. Conversion Quick Facts
- 1 km = 1,000 m
- 1 m = 100 cm
- 1 cm = 10 mm
- 1 kg = 1,000 g
- 1 L = 1,000 mL
Example:
Convert 4.5 km to meters.
▶️ Answer/Explanation
1 km = 1,000 m
So, 4.5 × 1,000 = 4,500 m
Example:
Convert 3,200 g to kg.
▶️ Answer/Explanation
1 kg = 1,000 g
So, 3,200 ÷ 1,000 = 3.2 kg
5. Temperature Conversions
Temperature can be converted using these formulas:
- \( °F = \dfrac{9}{5}°C + 32 \)
- \( °C = \dfrac{5}{9}(°F – 32) \)
- \( K = °C + 273.15 \)
Example:
Convert 25°C to °F and K.
▶️ Answer/Explanation
\( °F = \dfrac{9}{5}(25) + 32 = 45 + 32 = 77°F \)
\( K = 25 + 273.15 = 298.15 K \)
6. Derived Units (Speed & Density)
- \( 1 \text{ km/h} = \dfrac{1000 \text{ m}}{3600 \text{ s}} = 0.2778 \text{ m/s} \)
- \( 1 \text{ m/s} = 3.6 \text{ km/h} \)
Example:
Convert 72 km/h to m/s.
▶️ Answer/Explanation
72 ÷ 3.6 = 20 m/s
7. Time Conversions
- 1 min = 60 s
- 1 hour = 60 min = 3,600 s
- 1 day = 24 hours
Example:
Convert 2.5 hours to minutes and seconds.
▶️ Answer/Explanation
Step 1: Convert hours to minutes → \( 2.5 \times 60 = 150 \, \text{minutes} \).
Step 2: Convert minutes to seconds → \( 150 \times 60 = 9{,}000 \, \text{seconds} \).
Final Answer: 150 minutes or 9,000 seconds.