Comparison
Beginner
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Scientific Notation and Engineering Notation Explained
Scientific notation expresses very large or very small numbers compactly. Engineering notation uses exponents that are multiples of three, aligning with SI prefixes like kilo, mega, and nano.
Key Takeaways
- Format: `a × 10^n` where 1 ≤ |a| < 10.
- Moving the decimal point right decreases the exponent.
- Like scientific notation but the exponent is always a multiple of 3 (...
- Multiply coefficients, add exponents:
- ## Engineering Notation Like scientific notation but the exponent is always a multiple of 3 (.
Scientific Notation
Format: a × 10^n where 1 ≤ |a| < 10.
| Number | Scientific Notation |
|---|---|
| 300,000,000 | 3.0 × 10⁸ |
| 0.0000042 | 4.2 × 10⁻⁶ |
| 1,500 | 1.5 × 10³ |
| 0.025 | 2.5 × 10⁻² |
Conversion Rules
Moving the decimal point right decreases the exponent. Moving it left increases the exponent. Each position shift changes the exponent by 1.
Engineering Notation
Like scientific notation but the exponent is always a multiple of 3 (... -6, -3, 0, 3, 6, 9 ...). The coefficient ranges from 1 to 999.
| Number | Scientific | Engineering |
|---|---|---|
| 0.0000042 | 4.2 × 10⁻⁶ | 4.2 × 10⁻⁶ (micro) |
| 0.025 | 2.5 × 10⁻² | 25 × 10⁻³ (milli) |
| 1,500 | 1.5 × 10³ | 1.5 × 10³ (kilo) |
| 47,000,000 | 4.7 × 10⁷ | 47 × 10⁶ (mega) |
SI Prefix Mapping
| Prefix | Symbol | Exponent |
|---|---|---|
| pico | p | 10⁻¹² |
| nano | n | 10⁻⁹ |
| micro | μ | 10⁻⁶ |
| milli | m | 10⁻³ |
| kilo | k | 10³ |
| mega | M | 10⁶ |
| giga | G | 10⁹ |
| tera | T | 10¹² |
Arithmetic with Scientific Notation
Multiplication
Multiply coefficients, add exponents:
(3 × 10⁴) × (2 × 10³) = 6 × 10⁷
Division
Divide coefficients, subtract exponents:
(6 × 10⁸) / (2 × 10³) = 3 × 10⁵
Addition / Subtraction
First align exponents, then add coefficients:
3.0 × 10⁴ + 5.0 × 10³ = 3.0 × 10⁴ + 0.5 × 10⁴ = 3.5 × 10⁴