Math · Physics · Science
Scientific
Notation Calculator
Convert numbers to and from scientific notation. Add, subtract, multiply, and divide in scientific notation with full step-by-step solutions and notable constants reference.
—
Coefficient
—
Exponent
—
Form
Convert Decimal ↔ Scientific Notation
3.14159
×
10
⁰
dec
— or enter in scientific notation —
× 10
Arithmetic in Scientific Notation
First Number (a × 10ⁿ)
× 10
Operation
Second Number (b × 10ᵐ)
× 10
sf
Result
📋 Step-by-Step
🔭 Notable Scientific Constants — Click to Load
📋 Powers of 10 Reference — Click to Convert
What Is Scientific Notation?
Scientific notation expresses numbers as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. It makes very large numbers (like the distance to the Sun: 1.496 × 10¹¹ m) and very small numbers (like the electron mass: 9.109 × 10⁻³¹ kg) easier to write and compare.
Scientific Notation Arithmetic Rules
Multiply: (a × 10ᵐ) × (b × 10ⁿ) = (a×b) × 10^(m+n)
Divide: (a × 10ᵐ) ÷ (b × 10ⁿ) = (a÷b) × 10^(m−n)
Add/Sub: Convert to same exponent, then add/subtract coefficients
3.2 × 10⁴ + 1.5 × 10³ = 3.2 × 10⁴ + 0.15 × 10⁴ = 3.35 × 10⁴
Normalize: Adjust so 1 ≤ |coefficient| < 10
25.4 × 10³ → 2.54 × 10⁴
What is the difference between scientific and engineering notation?
Scientific notation uses any exponent (1 ≤ coefficient < 10), so 47,000 = 4.7 × 10⁴. Engineering notation restricts exponents to multiples of 3 (matching SI prefixes), so 47,000 = 47 × 10³ = 47 kilo. Engineering notation is used in electronics and SI unit systems because 10³=kilo, 10⁶=mega, 10⁹=giga, etc.
How do you convert scientific notation to decimal?
Move the decimal point in the coefficient by the exponent value. If n is positive, move right (number gets larger). If n is negative, move left (number gets smaller). For example: 3.45 × 10³ → move decimal 3 places right → 3450. And 3.45 × 10⁻³ → move decimal 3 places left → 0.00345.
What is E notation and how does it relate to scientific notation?
E notation (or exponential notation) uses E instead of × 10^, making it typeable in plain text and programming languages. 3.45 × 10⁸ = 3.45E8 = 3.45e8. This is the format used in calculators, Excel, Python, and scientific software. It means exactly the same thing as scientific notation.
Why do scientists use scientific notation?
Scientific notation prevents errors when writing very large or small numbers. The number of atoms in a gram of hydrogen is 602,200,000,000,000,000,000,000 — easy to miscopy. As 6.022 × 10²³ it's unambiguous and the magnitude (10²³) is immediately visible. Scientific notation also makes it easy to compare magnitudes: 10²³ is clearly much larger than 10¹⁵, whereas counting zeros is error-prone.