Standard Form (Scientific Notation)
Learn how to write very large and very small numbers in standard form (A x 10^n). With real-world examples from science and space.
How do you write the distance from Earth to the Sun? It's 149,600,000,000 metres. That's a pain to write out. Standard form fixes this: 1.496 × 10¹¹ m.
The Format
A × 10ⁿ where 1 ≤ A < 10 and n is an integer
A must be between 1 and 10 (including 1, but not 10). n tells you how many places to move the decimal point.
Big Numbers — Positive n
A positive power means a big number. Count how many places you move the decimal point to the right.
Worked Example 1 — Converting a Big Number
Write 3,500,000 in standard form.
- Put the decimal after the first non-zero digit: 3.5
- Count how many places: 3.500000 → 6 places to the right
- Answer: 3.5 × 10⁶
Small Numbers — Negative n
A negative power means a small number (less than 1). Count how many places you move the decimal point to the left.
Worked Example 2 — Converting a Small Number
Write 0.00042 in standard form.
- Put the decimal after the first non-zero digit: 4.2
- Count how many places: 0.00042 → 4 places to the left
- Answer: 4.2 × 10⁻⁴
Calculations in Standard Form
Worked Example 3 — Multiplying
(3 × 10⁴) × (2 × 10⁵)
- Multiply the numbers: 3 × 2 = 6
- Add the powers: 4 + 5 = 9
- Answer: 6 × 10⁹
For division: divide the numbers and subtract the powers.
Real-World Examples
| Thing | Value | Standard Form |
|---|---|---|
| Distance to Sun | 149,600,000,000 m | 1.496 × 10¹¹ m |
| Width of human hair | 0.00007 m | 7 × 10⁻⁵ m |
| World population | 8,100,000,000 | 8.1 × 10⁹ |
| Size of an atom | 0.0000000001 m | 1 × 10⁻¹⁰ m |
Try It Yourself
- Write 72,000 in standard form. (Answer: 7.2 × 10⁴)
- Write 0.0061 in standard form. (Answer: 6.1 × 10⁻³)
- Calculate (4 × 10³) × (5 × 10⁶). (Answer: 2 × 10¹⁰)