🔬 Scientific Notation: A Complete Guide for Students (With Examples & Quizzes)

🌍 Introduction

In science, we often deal with numbers that are extremely large (like distance between planets 🌍➡️☀️) or extremely small (like atom size ⚛️).
Writing these numbers normally is:

• Hard to read 👀

• Time-consuming ✍️

• Difficult for calculations 🧮

👉 Solution: Scientific Notation — a smart way to write numbers using powers of 10.

🧠 What Is Scientific Notation?

Scientific notation expresses a number in the form:

A × 10ⁿ

Where:

• A = a number between 1 and 9.99…

• n = exponent (power) of 10

📐 Rules for Writing Scientific Notation

1️⃣ Move the decimal until 1 non-zero digit remains on the left
2️⃣ Count how many places you moved
3️⃣

• If you moved left → exponent positive

• If you moved right → exponent negative

🌞 Real-World Example 1: Distance from Sun to Earth

Normal form:
138,000,000 km

Steps:

• 138,000,000 → 1.38

• Decimal moved 8 places left

• Scientific form:
  1.38 × 10⁸ km ✔️

Since the number is large → positive exponent

⚛️ Example 2: Diameter of a Hydrogen Atom

Normal form:
0.000000000052 m

Steps:

• 0.000000000052 → 5.2

• Decimal moved 11 places right

• Scientific form:
  5.2 × 10⁻¹¹ m ✔️

Small number → negative exponent

⚡ Fun Fact

Kilogram (kg) is the only SI base unit with a prefix.
The actual base unit is gram (g), but history made kg standard.

🏷️ SI Prefixes (Multiples & Submultiples)

🧭 Real-World Prefix Conversions

1️⃣ Millimetres → Metres

5000 mm = 5 m
📱 Smartphone width ≈ 75 mm = 0.075 m

2️⃣ Centimetres → Metres

175 cm = 1.75 m
👤 Human height

3️⃣ Grams → Kilograms

3000 g = 3 kg
💻 Laptop ≈ 2 kg

4️⃣ Microseconds → Seconds

2000 μs = 2 × 10⁻³ s = 2 ms
🖥️ CPU timing

5️⃣ Kilometres → Metres

5 km = 5000 m
🏃 5K Race

6️⃣ Nanometres → Metres

7 nm = 7 × 10⁻⁹ m
📱 Processor technology

🧮 Operations in Scientific Notation

➕ 1️⃣ Addition & Subtraction

Make exponents the same first.

Example:

5.123 × 10⁴ + 3.28 × 10⁵
3.28 × 10⁵ = 32.8 × 10⁴

Add:
(5.123 + 32.8) × 10⁴
= 37.923 × 10⁴
= 3.7923 × 10⁵ ✔️

✖️ 2️⃣ Multiplication

Multiply coefficients, add exponents.

(4 × 10³) × (6 × 10⁶)
= 24 × 10⁹
= 2.4 × 10¹⁰

➗ 3️⃣ Division

Divide coefficients, subtract exponents.

(6 × 10⁶) ÷ (2 × 10⁻²)
= 3 × 10⁸ ✔️

🎯 Quiz 1: Convert to Scientific Notation

💡 Fun: 1.86 × 10⁵ m/s ≈ Speed of Light (in km/s)

🎯 Quiz 2: 100 m equals?

Correct answer:
✔️ (c) 100,000 mm

Reason:
100 m = 100 × 1000 mm = 100,000 mm

🧠 Memory Trick

“King Henry Died By Drinking Chocolate Milk”
Kilo → Hecto → Deka → Base → Deci → Centi → Milli

📝 Summary

✅ Scientific Notation:

• Makes large & small numbers easy

• Uses powers of 10

• Positive exponent → large number

• Negative exponent → small number

✅ SI Prefixes:

• Help convert between scales

• Used in science, technology & engineering

✅ Operations:

• Add/Subtract → equal exponents

• Multiply → add exponents

• Divide → subtract exponents

🚀 Your Turn: Take My Test

(You can send your questions anytime, and I’ll grade them!)