Scientific Notation Calculator
Convert numbers to and from scientific notation.
Input Number
Scientific Notation
Standard form
Coefficient
Mantissa
Exponent
Power of 10
Engineering Notation
Powers of 3
Magnitude
How it works
Scientific notation writes very large or very small numbers compactly as a value between 1 and 10 multiplied by a power of ten. The exponent counts how many places the decimal moves — positive for big numbers, negative for small ones.
Scientific notation
n = a × 10ᵇ where 1 ≤ |a| < 10
- a
- the coefficient (mantissa)
- b
- the exponent (decimal places moved)
Worked example
- Write 45,000 in scientific notation
- Move the decimal 4 places left: 4.5
- That's ×10⁴
45,000 = 4.5 × 10⁴.
Good to know
- Small numbers use negative exponents: 0.00067 = 6.7 × 10⁻⁴.
- To multiply, multiply the coefficients and add the exponents; to divide, divide and subtract.
- It's the standard way to express significant figures cleanly in science and engineering.
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Frequently Asked Questions
How do I write numbers in scientific notation?
Format: a × 10^n where 1 ≤ a < 10. Example: 1,500 = 1.5 × 10³, 0.005 = 5 × 10⁻³. Move decimal to get coefficient between 1-10.
When should I use scientific notation?
Use for very large (astronomy, chemistry) or very small numbers (atomic scale, electronics). Makes calculations easier and reduces errors with many zeros.
How do I multiply numbers in scientific notation?
Multiply coefficients and add exponents: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. For division, divide coefficients and subtract exponents.