Scientific Notation Calculator
Very large and very small numbers are unreadable in full. Scientific notation makes their size obvious at a glance.
Last updated: August 2026 · Written and verified by Akash Pandey
Convert to or from scientific notation
Result
This runs the same calculation engine as the main scientific calculator, entirely in your browser. Nothing you type is sent anywhere.
The format
Scientific notation - also called standard form - writes every number as a single digit before the decimal point, multiplied by a power of ten.
m × 10ⁿ, where 1 ≤ |m| < 10 and n is a whole number
- m is the mantissa (or significand) - exactly one non-zero digit before the point
- n is the exponent - positive for large numbers, negative for small ones
- The exponent counts how many places the decimal point moved.
The constraint on m is what makes the form standard. 14.96 × 10⁷ and 0.1496 × 10⁹ are the same quantity, but only 1.496 × 10⁸ is in scientific notation, so two numbers written that way can always be compared by their exponents first.
Worked examples
Write 149,600,000 in scientific notation
149600000
- Place the decimal point after the first non-zero digit:
1.496. - Count how many places it moved: from after the final 0 to after the 1 is 8 places left.
- Moving left gives a positive exponent.
- This is the mean Earth–Sun distance in kilometres.
= 1.496 × 10⁸
- Place the decimal point after the first non-zero digit:
Write 0.00000042 in scientific notation
0.00000042
- The first non-zero digit is 4, so the mantissa is
4.2. - The point moved 7 places to the right to get there.
- Moving right gives a negative exponent.
= 4.2 × 10⁻⁷
- The first non-zero digit is 4, so the mantissa is
Convert 3.2 × 10⁵ back to a decimal
3.2 × 10^5
- A positive exponent of 5 moves the decimal point 5 places right.
3.2→32→320→3200→32000→320000.- Pad with zeros as needed.
= 320,000
Multiply (3 × 10⁴) by (2 × 10⁻⁶)
(3 × 10^4) × (2 × 10^-6)
- Multiply the mantissas:
3 × 2 = 6. - Add the exponents:
4 + (−6) = −2. - That gives
6 × 10⁻², already in standard form. - As a decimal, 0.06.
= 6 × 10⁻²
- Multiply the mantissas:
Arithmetic in scientific notation
| Operation | Rule | Example |
|---|---|---|
| Multiply | multiply mantissas, add exponents | (2×10³)(4×10⁵) = 8×10⁸ |
| Divide | divide mantissas, subtract exponents | (8×10⁵)/(2×10³) = 4×10² |
| Power | raise mantissa, multiply exponent | (2×10³)² = 4×10⁶ |
| Add / subtract | match exponents first, then add mantissas | 2×10³ + 3×10² = 2.3×10³ |
Significant figures
Scientific notation makes significant figures unambiguous, which is its second real advantage. Written plainly, 1500 could carry two, three or four significant figures - there is no way to tell whether the trailing zeros are measured or merely placeholders. Written as 1.5 × 10³ it is unambiguously two; as 1.500 × 10³, unambiguously four.
- Every digit in the mantissa is significant, including trailing zeros.
- The exponent is never counted - it records scale, not precision.
- When multiplying or dividing, the result carries as many significant figures as the least precise input.
- When adding or subtracting, it is decimal places that govern, not significant figures.
Scale reference
| Quantity | Scientific notation | Prefix |
|---|---|---|
| Diameter of a proton (m) | 1.7 × 10⁻¹⁵ | femto |
| Diameter of a hydrogen atom (m) | 1.06 × 10⁻¹⁰ | — |
| Wavelength of green light (m) | 5.5 × 10⁻⁷ | — |
| Human hair width (m) | 7 × 10⁻⁵ | micro |
| Speed of light (m/s) | 3.00 × 10⁸ | — |
| Earth–Sun distance (km) | 1.496 × 10⁸ | — |
| Avogadro's number | 6.022 × 10²³ | — |
| Mass of the Earth (kg) | 5.97 × 10²⁴ | — |
The main calculator has a SCI toggle that switches every result into this form, which is often the only way to read an answer that has run to fifteen digits.
Frequently Asked Questions
What is scientific notation?
A way of writing numbers as m × 10ⁿ, where the mantissa m has exactly one non-zero digit before the decimal point. It makes very large and very small numbers readable and comparable.
How do I convert a decimal to scientific notation?
Move the decimal point until exactly one non-zero digit sits before it, then count the places moved. Moving left gives a positive exponent, moving right a negative one.
What is the difference between scientific notation and standard form?
They are the same thing. "Standard form" is the usual name in British and Commonwealth schools; "scientific notation" is more common in the United States.
What does E notation mean, as in 1.496E8?
It is scientific notation written for a keyboard - the E stands for "times ten to the power of". 1.496E8 means 1.496 × 10⁸. Calculators and programming languages use it because superscripts are hard to type.
Why does my calculator switch to scientific notation on its own?
Because past a certain magnitude the digits would no longer all be reliable. This calculator switches above 2⁵³ − 1 for integers, and for very small values below 10⁻⁶, so it never displays precision it does not have.
How do I add two numbers in scientific notation?
Rewrite them with the same exponent first, then add the mantissas. 2×10³ + 3×10² becomes 2×10³ + 0.3×10³ = 2.3×10³.
How many significant figures does scientific notation preserve?
All the digits in the mantissa are significant. 3.00 × 10⁸ has three significant figures; 3 × 10⁸ has one. The notation itself does not add or remove precision - it is a transparent way to show exactly how many figures are meaningful.
Why is scientific notation used in science and engineering?
Because many physical quantities span enormous ranges - the mass of an electron versus the mass of the Sun, or the speed of light versus the thickness of a hair. Scientific notation keeps the significant digits front and centre while the exponent tracks the scale.