Standard Form: The Sci-Fi Scale
Edexcel 4MA1 | Topic 1.9 | From Atoms to Planets
The Sci-Fi Scale
Macroscopic
3 × 104
= 30,000
10-9 (Atom)100 (Human)109 (Planet)
The Logic Track
📏 The Range Rule
The first number (coefficient A) MUST be between 1 and 10.
✗ 0.5 × 10⁴ (too small)
✗ 12 × 10⁴ (too big)
✓ 5 × 10⁴ (perfect!)
🎯 The Adjustment Rule
When you move the decimal point:
LEFT is LIFT ↑
Move decimal left → Power goes UP
45 × 10⁵ → 4.5 × 10⁶
RIGHT is REDUCE ↓
Move decimal right → Power goes DOWN
0.45 × 10⁵ → 4.5 × 10⁴
⚡ The "Matching Powers" Rule
You can't add x² and x³. You can't add 10⁴ and 10⁵.
Make the powers match first!
Example:
(3 × 10⁴) + (2 × 10⁵)
→ (0.3 × 10⁵) + (2 × 10⁵)
→ 2.3 × 10⁵
Your Current Number:
3 × 104 represents 30,000 – a number in the macroscopic range.
The Dynamic Solver
× 10
× 10
Cambridge Mark Scheme Working:
Step 1: Numbers
2 × 8 = 16.00
Step 2: Powers
105 × 106 = 1011
(Add powers: 5 + 6 = 11)
Step 3: Combined
16.00 × 1011
Step 4: Fix RangeGrade 9
1.60 × 1012
(Moved decimal LEFT → Power UP)
FINAL ANSWER:
1.60 × 1012
Edexcel 4MA1 Foundation & Higher Tier | Specification A (2018-2028)
Standard Form enables us to write very large or very small numbers efficiently
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