Scientific Notation Calculator — Convert, Add, Multiply & Divide
Convert numbers to and from scientific notation and perform arithmetic. Covers standard form, engineering notation, rules for multiplication and division, with examples.
The distance from Earth to the Sun is 149,600,000,000 meters. An electron's mass is 0.000000000000000000000000000000911 kg. Writing these out is painful and error-prone — scientific notation is how scientists and engineers avoid this. Convert and calculate with the CalcHub Scientific Notation Calculator.
What Is Scientific Notation?
A number in scientific notation has the form:
a × 10ⁿWhere 1 ≤ |a| < 10 (the coefficient, also called mantissa or significand) and n is an integer exponent.
Large numbers: positive exponent 93,000,000 miles = 9.3 × 10⁷ miles Small numbers: negative exponent 0.00000045 = 4.5 × 10⁻⁷Converting to Scientific Notation
Count how many places you move the decimal point to get a coefficient between 1 and 10.
Example: 0.00362 Move decimal right 3 places: 3.62 Result: 3.62 × 10⁻³ Example: 47,500,000 Move decimal left 7 places: 4.75 Result: 4.75 × 10⁷ Example: 0.1 Move right 1 place: 1.0 Result: 1.0 × 10⁻¹Converting from Scientific Notation to Standard Form
Move the decimal point by the exponent value.
5.8 × 10⁴: Move decimal right 4 → 58,000 2.03 × 10⁻³: Move decimal left 3 → 0.00203Arithmetic with Scientific Notation
Multiplication
Multiply the coefficients, add the exponents. (3.0 × 10⁵) × (2.0 × 10³) = (3.0 × 2.0) × 10⁵⁺³ = 6.0 × 10⁸ (4.5 × 10⁶) × (3.0 × 10⁻²) = 13.5 × 10⁴ = 1.35 × 10⁵ (adjust coefficient back to 1–10)Division
Divide the coefficients, subtract the exponents. (8.4 × 10⁷) ÷ (2.1 × 10³) = (8.4 ÷ 2.1) × 10⁷⁻³ = 4.0 × 10⁴Addition and Subtraction
Make the exponents equal first, then add/subtract the coefficients. (3.2 × 10⁵) + (4.7 × 10⁴) = (3.2 × 10⁵) + (0.47 × 10⁵) = (3.2 + 0.47) × 10⁵ = 3.67 × 10⁵Engineering Notation Variant
Engineering notation restricts the exponent to multiples of 3 (matching SI prefixes). This makes it easier to state values in kilo-, mega-, giga-, etc.
| Engineering Form | Standard Prefix |
|---|---|
| × 10³ | kilo (k) |
| × 10⁶ | mega (M) |
| × 10⁹ | giga (G) |
| × 10¹² | tera (T) |
| × 10⁻³ | milli (m) |
| × 10⁻⁶ | micro (μ) |
| × 10⁻⁹ | nano (n) |
| × 10⁻¹² | pico (p) |
Scale Reference: Famous Numbers
| Quantity | Value | Scientific Notation |
|---|---|---|
| Avogadro's number | 602,200,000,000,000,000,000,000 | 6.022 × 10²³ |
| Speed of light | 299,792,458 m/s | ≈ 3.0 × 10⁸ m/s |
| Electron mass (kg) | 0.000...000911 (31 zeros) | 9.11 × 10⁻³¹ |
| Age of universe (years) | 13,800,000,000 | 1.38 × 10¹⁰ |
| Planck length (m) | 0.000...0162 (34 zeros) | 1.62 × 10⁻³⁵ |
Why is the coefficient always between 1 and 10?
Convention. Any number can be written in scientific notation — 0.5 × 10⁶ and 5 × 10⁵ are mathematically equal. The 1 ≤ |a| < 10 rule ensures a unique, unambiguous representation for every number, making comparison and computation consistent.
What is E notation in calculators and programming?
"E notation" is scientific notation without the × 10 — it's shorthand for digital displays and code. 4.5E6 = 4.5 × 10⁶. Python, JavaScript, Excel, and most calculators accept this format. E8 on your calculator display means × 10⁸, not a letter E.
How does scientific notation preserve significant figures?
It handles the ambiguity of trailing zeros cleanly. 1500 might have 2, 3, or 4 sig figs — but 1.500 × 10³ unambiguously has 4 sig figs, and 1.5 × 10³ has 2. This is why scientists always use scientific notation when precision matters.