PRACTICAL GUIDES · Math and geometry
How to write scientific notation, step by step
Move the decimal point, choose the exponent sign and reconstruct the original number. Examples cover large, small and negative values.
By Puffinmint · Updated
Coefficient, power of ten and sign
Scientific notation separates a coefficient from a power of ten. For a nonzero value, the coefficient’s absolute value is at least one and less than ten. A negative number keeps its sign on the coefficient.
Move the decimal point and reconstruct the value
Move the decimal point until exactly one nonzero digit precedes it. Count the moves: moving left gives a positive exponent, moving right gives a negative exponent. The number’s sign and the exponent’s sign are independent.
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Input
0.0000123
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Calculation steps
Choose and apply the method
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Result
1.23 × 10⁻⁵
TRY THIS STEP
Scientific notation converter
Work inside this guide: load an example, run the tool and edit the inputs to compare results. The second experiment tests a different case.
A reproducible example
For 0.0000123, move the point five places right to obtain 1.23 with exponent −5. For 123000, move it five places left to obtain 1.23 with exponent 5. Reconstruct the original number as a final check.
Convert a large negative number
Load −123000: the coefficient is −1.23 and the exponent is 5. A negative number does not require a negative exponent. Enter −1.23e5 and check that the decimal value remains −123000.
Result
Enter your values to see the result.
Normalize 0.0000123 and 123000
For 0.0000123, move the point five places right to obtain 1.23 with exponent −5. For 123000, move it five places left to obtain 1.23 with exponent 5. Reconstruct the original number as a final check.
Usage scenario
- Input
- 0.0000123
- Result
Calculation steps
Normalize the coefficient between 1 and 10
Reconstruct the original number
Numerical value versus significant figures
The converter normalizes trailing zeros and treats the input as an exact numeric value rather than a statement of experimental precision. For example, 1.20 and 1.2 have the same value but can communicate different significant figures in a measurement.
These are example inputs, rather than measurements of a real case. Results use the full tool’s calculation engine. Compare them with the worked steps in this guide, then tick the checks after reviewing.
| Parameter | Value |
|---|---|
| What are the limits of this tool? | At most 1,000 digits; normalized exponent from −10,000 to 10,000. Zeros are normalized; significant figures are not inferred. |
| Processing and privacy | Inputs and results are processed in your browser and are not sent to the server. Aggregate statistics, when enabled, record only the tool and outcome, without the content. |