About the Scientific Notation Calculator
Scientific notation writes any number as a value between 1 and 10 multiplied by a power of ten. It is how science and engineering handle quantities that would otherwise need long strings of zeros, and it makes the significant digits and the magnitude immediately visible.
The formula
n = m × 10ᵉ, where 1 ≤ |m| < 10m is the mantissa or coefficient, carrying the significant digits. e is the exponent, giving the order of magnitude — positive for large numbers, negative for small ones.
How to use this calculator
- 1Enter your Number. The field starts at
0.000045, which you can overwrite. - 2Enter your Significant Figures. The field starts at
3, which you can overwrite. - 3Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Number | 0.000045 |
| Significant Figures | 3 |
Result
Scientific Notation: 4.50e-5
Formatted: 4.50 × 10^-5
Engineering Notation: 45.00 × 10^-6
Decimal: 0.000045
log₁₀: -4.346787
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
The exponent counts how far the decimal point moves. 0.000045 becomes 4.5 × 10⁻⁵, since the point shifts five places right; 45,000 becomes 4.5 × 10⁴, shifting four places left. Negative exponents mean small numbers, and this is the single most common source of confusion.
The notation also makes significant figures explicit, which ordinary decimal form cannot. Writing 4,500 leaves it ambiguous whether the trailing zeros are measured or merely placeholders. Writing 4.5 × 10³ states two significant figures and 4.500 × 10³ states four — a distinction that matters throughout experimental science.
Things worth knowing
- The mantissa must have exactly one non-zero digit before the decimal point. 45 × 10³ is valid arithmetic but not proper scientific notation.
- Multiplying means multiplying mantissas and adding exponents; dividing means dividing mantissas and subtracting exponents.
- Calculators display this as E notation: 4.5E-5 means 4.5 × 10⁻⁵.
- Engineering notation restricts exponents to multiples of three so they align with prefixes like kilo, mega, and milli.
- To add or subtract, first convert both values to the same exponent.
Frequently asked questions
How do I write a number in scientific notation?+
Move the decimal point until exactly one non-zero digit remains in front of it, then record how many places you moved as the exponent. Moving left gives a positive exponent, moving right a negative one.
What does a negative exponent mean?+
That the number is smaller than 1. 3 × 10⁻⁴ is 0.0003 — the exponent counts how many places the decimal point moves left from the mantissa.
What does E mean on a calculator display?+
It is shorthand for "times ten to the power of". 2.5E6 means 2.5 × 10⁶, or 2,500,000. Calculators switch to this format when a number is too long to display.
How do I multiply numbers in scientific notation?+
Multiply the mantissas and add the exponents. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. If the resulting mantissa reaches 10 or more, shift it and increment the exponent.