Scientific Notation Converter (bidirectional)
Convert a decimal number to scientific notation (a × 10^b) or rebuild a decimal from a coefficient and exponent, with worked examples and rules.
Results
Scientific notation
- Coefficient a
- 1.23456
- Exponent b
- 5
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Educational estimates · not financial advice · free, no signup
Formula / how it works
to_sci: exp = floor(log10|n|), coef = n / 10^exp. from_sci: decimal = coef * 10^exp.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Scientific notation writes very large or very small numbers compactly as a coefficient between 1 and 10 multiplied by a power of ten. The speed of light, 299,792,458 m/s, becomes about 3.0 × 10⁸; the size of a bacterium, 0.000002 m, becomes 2 × 10⁻⁶. The notation makes magnitudes easy to compare and avoids miscounting zeros. This converter works in both directions. Enter a decimal to get the coefficient and exponent, or enter a coefficient and exponent to get the full decimal. Students use it in science and maths, and engineers use it to read calculator and spreadsheet output such as 1.23E+5.
When to use / who it helps
- You need to write a very large or small number compactly.
- You are converting calculator output like 1.2E-4 to a decimal.
- You are checking homework in physics or chemistry.
- You are comparing orders of magnitude.
- You are preparing numbers for a report using significant figures.
How to use
Steps
- Choose the direction, decimal to scientific or scientific to decimal.
- For decimal to scientific, enter the number in the value field.
- For scientific to decimal, enter the coefficient and the exponent.
- Read the notation, coefficient and exponent.
- Check that the coefficient lies between 1 and 10.
- Round the coefficient to the appropriate significant figures.
How to interpret results
- A positive exponent means a number of 10 or more; a negative exponent means a number below 1.
- The exponent counts how many places the decimal point moved.
- The coefficient carries the significant digits.
- Calculators show E notation, where 1.2E-4 means 1.2 × 10⁻⁴.
- Rounding the coefficient changes the precision, not the magnitude.
Common mistakes & gotchas
- Leaving the coefficient outside the range of 1 to 10.
- Getting the sign of the exponent wrong when the number is below 1.
- Confusing E notation with Euler's number e.
- Counting places incorrectly.
- Losing significant figures when rounding.
Worked example
Worked example — 123,456 and 0.00042
- 123,456: move the decimal point 5 places left to get 1.23456, so 123,456 = 1.23456 × 10⁵.
- 0.00042: move the decimal point 4 places right to get 4.2, so 0.00042 = 4.2 × 10⁻⁴.
- Reverse: 3.2 × 10⁶ means move the decimal point 6 places right, giving 3,200,000.
- Check: 1.23456 × 100,000 = 123,456.
Result: 123,456 is 1.23456 × 10⁵, matching the tool's default.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
to_sci: exp = floor(log10|n|), coef = n / 10^exp. from_sci: decimal = coef * 10^exp.
Frequently asked questions
What is scientific notation?
A way to write numbers as a coefficient between 1 and 10 times a power of ten.
How do I convert a small number?
Move the decimal point to the right until you have a number between 1 and 10, and use a negative exponent equal to the places moved.
What does 1.2E5 mean?
1.2 × 10⁵, which is 120,000.
How do significant figures work with it?
The coefficient's digits show the precision, so write only the significant digits.
Is 12 × 10³ valid?
It is a number, but standard form requires a coefficient between 1 and 10, so write 1.2 × 10⁴.
Can I enter negative numbers?
Yes, the sign applies to the coefficient.