PTCB Physics 2025 Scientific Notation Guide | PTCB 9th Physics SI Units & Prefixes

PTCB Physics 2025 Scientific Notation Guide | PTCB 9th Physics SI Units & Prefixes

🔢 Scientific Notations 🌍 Introduction

When numbers are very large 🐘 or very small 🐜, writing them normally:

• Takes a lot of space 📏
• Is hard to read 👀
• Makes calculations difficult 🧮

Solution? Scientists use scientific notation! 🎯

📐 Rules for Scientific Notation:

1. The number is written as a value from 1 to 9.99... × 10 to some power
2. Move the decimal point until only one non-zero digit is on the left
3. The number of places the decimal is moved becomes the exponent of 10

🧮 Real-World Example 1: Sun to Earth Distance ☀️➡️🌍

Problem: Average distance from Sun to Earth

Normal form: 138,000,000 km

Step-by-step conversion:

1. Start with: 138,000,000
2. Move decimal 8 places to the left: 1.38
3. Count the moves: 8 places
4. Write in scientific notation: 1.38 × 10⁸ km ✅

Why positive exponent? Because the original number was greater than 1 📈

🧪 Real-World Example 2: Hydrogen Atom Diameter ⚛️

Problem: Diameter of hydrogen atom

Normal form: 0.000000000052 m

Step-by-step conversion:

1. Start with: 0.000000000052
2. Move decimal 11 places to the right: 5.2
3. Count the moves: 11 places
4. Write in scientific notation: 5.2 × 10⁻¹¹ m ✅

Why negative exponent? Because the original number was less than 1 📉

⚡ Quick Fact 💡

The kilogram is the only base SI unit that already has a prefix ("kilo-" means 1000).

The actual base unit is technically the gram, but for historical reasons, we use kilogram as the SI base unit! 🤔

🏷️ SI Prefixes and Multiples

SI units are often combined with prefixes to represent very large or very small numbers:

Prefix Symbol Power of 10 Decimal Value Memory Trick 🧠 atto a 10⁻¹⁸ 0.000000000000000001 Atomically tiny femto f 10⁻¹⁵ 0.000000000000001 Fantastically small pico p 10⁻¹² 0.000000000001 Pinhead size nano n 10⁻⁹ 0.000000001 Nanoscale 🔬 micro μ 10⁻⁶ 0.000001 Microscopic milli m 10⁻³ 0.001 Millipede legs centi c 10⁻² 0.01 Centipede 🐛 deci d 10⁻¹ 0.1 Decimal — — 10⁰ 1 Base unit kilo k 10³ 1,000 Kilometre walk 🚶 mega M 10⁶ 1,000,000 Mega stadium 🏟️ giga G 10⁹ 1,000,000,000 Gigantic storage 💾 tera T 10¹² 1,000,000,000,000 Terrifyingly big peta P 10¹⁵ 1,000,000,000,000,000 Peta-byte data exa E 10¹⁸ 1,000,000,000,000,000,000 Extremely huge 🌌

🧭 Real-World Examples of Prefixes 1️⃣ Millimetres → Metres 📏 5000 mm = 5000 ÷ 1000 = 5 m

Example: Width of a smartphone 📱 ≈ 75 mm = 0.075 m

2️⃣ Centimetres → Metres 📐 50,000 cm = 50,000 ÷ 100 = 500 m

Example: Height of a person 👤 ≈ 175 cm = 1.75 m

3️⃣ Grams → Kilograms ⚖️ 3000 g = 3000 ÷ 1000 = 3 kg

Example: A laptop 💻 ≈ 2000 g = 2 kg

4️⃣ Microseconds → Seconds ⏱️ 2000 μs = 2000 × 10⁻⁶ s = 2 × 10⁻³ s = 2 ms

Example: CPU instruction time 🖥️ ≈ 1-10 nanoseconds

5️⃣ Kilometres → Metres 🚗 5.5 km = 5.5 × 1000 = 5500 m

Example: A 5K race 🏃 = 5 km = 5000 m

6️⃣ Nanometres in Technology 🔬 7 nm chip = 7 × 10⁻⁹ m

Example: Modern smartphone processors use 5 nm technology! 📱

📝 Operations with Scientific Notation 1️⃣ Addition & Subtraction ➕➖

Rule: Make the exponents the same first, then add/subtract the coefficients.

Example 1(a): 5.123 × 10⁴ m + 3.28 × 10⁵ m

Step-by-step:

1. Make exponents equal: 3.28 × 10⁵ = 32.8 × 10⁴
2. Add coefficients: (5.123 + 32.8) × 10⁴ = 37.923 × 10⁴
3. Convert to proper form: 3.7923 × 10⁵ m ✅

Real-world: Adding distances: 51.23 km + 328 km = 379.23 km 🚗

Example 1(b): 2.57 × 10⁻² mm - 3.43 × 10⁻³ mm

Step-by-step:

1. Make exponents equal: 3.43 × 10⁻³ = 0.343 × 10⁻²
2. Subtract: (2.57 - 0.343) × 10⁻² = 2.227 × 10⁻² mm
3. Convert to metres: 2.227 × 10⁻⁵ m ✅

Real-world: Measuring tiny differences in wire thickness 🔧

2️⃣ Multiplication ✖️

Rule: Multiply coefficients, add exponents.

Example 2(a): (4 × 10³ kg) × (6 × 10⁶ m)

Step-by-step:

1. Multiply coefficients: 4 × 6 = 24
2. Add exponents: 10³⁺⁶ = 10⁹
3. Combine: 24 × 10⁹
4. Proper form: 2.4 × 10¹⁰ kg·m ✅

Real-world: Calculating momentum or energy 🚀

3️⃣ Division ➗

Rule: Divide coefficients, subtract exponents.

Example 2(b): (6 × 10⁶ m³) ÷ (2 × 10⁻² m²)

Step-by-step:

1. Divide coefficients: 6 ÷ 2 = 3
2. Subtract exponents: 10⁶⁻⁽⁻²⁾ = 10⁶⁺² = 10⁸
3. Subtract unit powers: m³⁻² = m¹
4. Result: 3 × 10⁸ m ✅

Real-world: Finding height when volume and area are known 📦

⚡ Quick Quiz Solutions 🎯 Quiz 1: Scientific Notation

Express the following into scientific notation:

(a) 0.00534 m Move decimal 3 places right → 5.34 × 10⁻³ m ✅ (b) 2574.32 kg Move decimal 3 places left → 2.57432 × 10³ kg ✅ (c) 0.45 m Move decimal 1 place right → 4.5 × 10⁻¹ m ✅ (d) 0.004 kg Move decimal 3 places right → 4 × 10⁻³ kg ✅ (e) 186000 s Move decimal 5 places left → 1.86 × 10⁵ s ✅

Fun fact: This is approximately the speed of light in km/s! 💡⚡

🎯 Quiz 2: Unit Conversion

100 m is equal to:

Let's check each option:

(a) 1000 μm ❌ 100 m = 100 × 10⁶ μm = 100,000,000 μm 1000 μm = 1 mm only INCORRECT (b) 1000 cm ❌ 100 m = 100 × 100 cm = 10,000 cm INCORRECT (c) 100,000 mm ✅ 100 m = 100 × 1000 mm = 100,000 mm CORRECT! ✅✅✅ (d) 1 km ❌ 100 m = 100 ÷ 1000 km = 0.1 km INCORRECT

Answer: (c) 100,000 mm 🎉

Real-world example: A football field 🏈 is about 100 m = 100,000 mm long!

🎓 Summary & Tips ✅ Key Takeaways:

1. Scientific notation makes big/small numbers manageable 📊
2. Positive exponents = large numbers (1) 📈
3. Negative exponents = small numbers (1) 📉
4. Addition/Subtraction = match exponents first ⚖️
5. Multiplication = multiply numbers, add exponents ✖️➕
6. Division = divide numbers, subtract exponents ➗➖

🧠 Memory Tricks:

• "King Henry Died By Drinking Chocolate Milk" 🍫🥛

  • Kilo, Hecto, Deka, Base, Deci, Centi, Milli

• Going right (smaller units) = multiply/move decimal right ➡️

• Going left (larger units) = divide/move decimal left ⬅️

🌟 Practice makes perfect! Try converting your everyday measurements into scientific notation! 🚀






Take My Test