Scientific Notation Calculator - Convert & Calculate E Notation Numbers
Input
Enter a number in standard or scientific notation (E notation supported)
Supported Formats:
- • Standard: 123000, 0.000123
- • E notation: 1.23E+5, 1.23E-4
- • Scientific: 1.23×10^5 (or 1.23×10^-4)
Quick Reference
Scientific Notation Rules
- • Mantissa must be between 1 and 10
- • Format: a × 10^n where 1 ≤ |a| < 10
- • Positive exponent: large numbers
- • Negative exponent: small numbers
- • E notation: 1.5E+10 = 1.5 × 10^10
Engineering Notation
- • Exponent is always a multiple of 3
- • Matches SI prefixes (k, M, G, m, μ, n)
- • Example: 1500 = 1.5 × 10^3 (1.5 k)
- • Easier for metric conversions
Multiplication Rule
- • (a × 10^m) × (b × 10^n)
- • = (a × b) × 10^(m+n)
- • Example: (2×10^3) × (3×10^4)
- • = 6 × 10^7
Division Rule
- • (a × 10^m) ÷ (b × 10^n)
- • = (a ÷ b) × 10^(m-n)
- • Example: (6×10^8) ÷ (2×10^3)
- • = 3 × 10^5
Understanding Scientific Notation
Scientific notation is a standardized way of writing numbers that makes very large or very small values more manageable. It expresses numbers in the form a × 10^n, where:
- a is the mantissa (coefficient): a number between 1 and 10
- n is the exponent (power of 10): an integer that can be positive or negative
Examples:
- • Large number: 5,000,000 = 5 × 10^6
- • Small number: 0.00003 = 3 × 10^-5
- • Speed of light: 299,792,458 m/s ≈ 3.00 × 10^8 m/s
- • Electron mass: 0.000000000000000000000000000000911 kg = 9.11 × 10^-31 kg
How to Convert Numbers
From Standard to Scientific Notation
- 1.Move the decimal point so that there is only one non-zero digit to the left of the decimal point.4,500 → 4.500 (moved 3 places left)
- 2.Count the places moved - this becomes your exponent.Moved 3 places → exponent is 3
- 3.Determine the sign: If you moved left (large number), exponent is positive. If moved right (small number), exponent is negative.4,500 = 4.5 × 10^3 (moved left → positive)
From Scientific to Standard Notation
- 1.Look at the exponent to determine which direction to move the decimal.6.7 × 10^4 → positive exponent, move right
- 2.Move the decimal that many places, adding zeros as needed.6.7 × 10^4 = 67,000 (moved 4 places right)
Arithmetic Operations
Multiplication
(a × 10^m) × (b × 10^n)
= (a × b) × 10^(m+n)
Example:
(3 × 10^5) × (2 × 10^3)
= (3 × 2) × 10^(5+3)
= 6 × 10^8
Division
(a × 10^m) ÷ (b × 10^n)
= (a ÷ b) × 10^(m-n)
Example:
(8 × 10^7) ÷ (2 × 10^3)
= (8 ÷ 2) × 10^(7-3)
= 4 × 10^4
Addition/Subtraction
First convert to the same exponent, then add/subtract mantissas.
Example:
(5 × 10^3) + (2 × 10^2)
= (5 × 10^3) + (0.2 × 10^3)
= 5.2 × 10^3
Adjusting Results
If mantissa ≥ 10 or < 1, adjust to proper form.
Example:
15 × 10^4 → adjust
= 1.5 × 10^5
E Notation vs Scientific Notation
E notation is a computer-friendly way to write scientific notation. The "E" stands for "exponent" or "× 10^".
| Standard | Scientific | E Notation |
|---|---|---|
| 6,020,000,000,000,000,000,000,000 | 6.02 × 10^23 | 6.02E+23 |
| 0.00000160 | 1.60 × 10^-6 | 1.60E-6 |
| 299,792,458 | 2.998 × 10^8 | 2.998E+8 |
Engineering Notation
Engineering notation is similar to scientific notation but restricts exponents to multiples of 3 (-12, -9, -6, -3, 0, 3, 6, 9, 12). This aligns with SI metric prefixes.
| Exponent | Prefix | Symbol | Example |
|---|---|---|---|
| 10^12 | tera | T | 1 TB = 1×10^12 bytes |
| 10^9 | giga | G | 1 GHz = 1×10^9 Hz |
| 10^6 | mega | M | 1 MW = 1×10^6 W |
| 10^3 | kilo | k | 1 km = 1×10^3 m |
| 10^-3 | milli | m | 1 ms = 1×10^-3 s |
| 10^-6 | micro | μ | 1 μm = 1×10^-6 m |
| 10^-9 | nano | n | 1 nm = 1×10^-9 m |
| 10^-12 | pico | p | 1 pF = 1×10^-12 F |