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 ร 10^n` where 1 โค |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 ร 10^n where 1 โค |a| < 10.
| Number | Scientific Notation |
|---|---|
| 300,000,000 | 3.0 ร 10โธ |
| 0.0000042 | 4.2 ร 10โปโถ |
| 1,500 | 1.5 ร 10ยณ |
| 0.025 | 2.5 ร 10โปยฒ |
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 ร 10โปโถ | 4.2 ร 10โปโถ (micro) |
| 0.025 | 2.5 ร 10โปยฒ | 25 ร 10โปยณ (milli) |
| 1,500 | 1.5 ร 10ยณ | 1.5 ร 10ยณ (kilo) |
| 47,000,000 | 4.7 ร 10โท | 47 ร 10โถ (mega) |
SI Prefix Mapping
| Prefix | Symbol | Exponent |
|---|---|---|
| pico | p | 10โปยนยฒ |
| nano | n | 10โปโน |
| micro | ฮผ | 10โปโถ |
| milli | m | 10โปยณ |
| kilo | k | 10ยณ |
| mega | M | 10โถ |
| giga | G | 10โน |
| tera | T | 10ยนยฒ |
Arithmetic with Scientific Notation
Multiplication
Multiply coefficients, add exponents:
(3 ร 10โด) ร (2 ร 10ยณ) = 6 ร 10โท
Division
Divide coefficients, subtract exponents:
(6 ร 10โธ) / (2 ร 10ยณ) = 3 ร 10โต
Addition / Subtraction
First align exponents, then add coefficients:
3.0 ร 10โด + 5.0 ร 10ยณ = 3.0 ร 10โด + 0.5 ร 10โด = 3.5 ร 10โด