Scientific Notation Calculator
Convert numbers to and from scientific notation, or multiply and divide numbers in scientific notation. Handles very large and very small numbers precisely.
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How to use this calculator
Scientific notation expresses any number as a coefficient (1 ≤ |a| < 10) multiplied by a power of 10. This makes very large or very small numbers compact and easy to compare.
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Choose an operation: convert to scientific notation, convert from scientific notation, or multiply/divide two values.
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Enter the required values — for conversions just enter the number; for multiply/divide enter both coefficients and exponents.
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The result is shown in both scientific notation and standard form with step-by-step working.
Frequently asked questions
Which fields does each operation use?
Standard → Scientific reads only the first field, the plain number. Scientific → Standard reads the first field as the coefficient and Exponent 1 as the power of ten. Multiply and Divide use all four fields. Fields an operation does not use are ignored, so stale values in them do no harm.
Why do I only get seven significant digits when converting a long number?
The coefficient is rounded to six decimal places, which is seven significant digits. 123,456,789 is shown as 1.234568 × 10^8, and the speed of light 299,792,458 as 2.997925 × 10^8. This is intentional rounding of the display, not a loss of the value itself, but you cannot read all nine digits back from the result.
Does the converter insist the coefficient be between 1 and 10?
Not when converting from scientific notation. Entering 45 with exponent 3 simply returns 45000 and echoes 45 × 10^3, without warning that the coefficient is outside the normal range. Multiply and divide results, and the Standard → Scientific mode, are always normalised to a coefficient with absolute value from 1 up to but not including 10.
What does multiply do with exponents?
It multiplies the coefficients, adds the exponents, and then renormalises. For 3 × 10^8 times 4 × 10^5, the working line shows (3 × 4) × 10^(8 + 5) = 12 × 10^13, and the result line renormalises that to 1.2 × 10^14. Divide subtracts exponents instead, and dividing by a coefficient of zero returns an error.
Why does a very small number show many zeros in Standard form?
The “Standard form” line writes the value out in full instead of switching to exponent notation. 1.6 × 10^−19 becomes 0.00000000000000000016, and 6.022 × 10^23 becomes 602200000000000000000000. Values are rounded to twelve significant digits first, and results too large or small for a double (around 10^±308) are not supported.
How are negative numbers and zero treated?
The sign stays on the coefficient: −0.000000789 gives −7.89 × 10^-7. Zero cannot be normalised, so it is reported as 0 × 10^0. Multiplying by a zero coefficient returns 0 with whatever exponent the exponents sum to, which is just a presentation quirk.
Can it add or subtract numbers in scientific notation?
No, only convert, multiply and divide. Addition and subtraction require the exponents to match first, which the tool does not do. For example, 3 × 10^5 + 4 × 10^4 means rewriting 4 × 10^4 as 0.4 × 10^5 before adding the coefficients to get 3.4 × 10^5.
Scientific notation: convert, multiply and divide
The normal form and how conversion works
A number in scientific notation has the shape a × 10^n with 1 ≤ |a| < 10. Moving the decimal point left to reach that coefficient raises the exponent, and moving it right lowers it. So 93,000,000 becomes 9.3 × 10^7 and 0.00045 becomes 4.5 × 10^-4. The converter reads the number, finds the correct exponent, and prints coefficient and exponent separately as well as together.
| Operation | Input | Result |
|---|---|---|
| Standard → scientific | 93000000 | 9.3 × 10^7 |
| Standard → scientific | 0.00045 | 4.5 × 10^-4 |
| Standard → scientific | −0.000000789 | −7.89 × 10^-7 |
| Scientific → standard | 6.022 × 10^23 | 602200000000000000000000 |
| Scientific → standard | 1.6 × 10^−19 | 0.00000000000000000016 |
Worked example: multiplying
Multiply 3 × 10^8 by 4 × 10^5. The coefficients give 12 and the exponents add to 13, so the raw answer is 12 × 10^13. That is not normal form, since 12 is above 10, so the result is renormalised to 1.2 × 10^14, which in full is 120000000000000. With negative exponents the same rules apply: 6.5 × 10^-4 times 2 × 10^-3 gives 13 × 10^-7, which becomes 1.3 × 10^-6 or 0.0000013.
Worked example: dividing
Divide 9.1 × 10^-31 by 1.6 × 10^-19. The coefficients give 5.6875 and the exponents subtract: −31 − (−19) = −12, so the answer is 5.6875 × 10^-12. Another case: 1 × 10^5 divided by 4 × 10^2 starts as 0.25 × 10^3, and normalising moves the decimal point one step right to 2.5 × 10^2, which is 250. The calculator shows both the raw working and the cleaned result.
Common slips
Forgetting to renormalise leaves answers like 12 × 10^13, which are correct but not standard. Subtracting a negative exponent is the next trap: −31 − (−19) is −12, not −50. Remember that a larger exponent does not always mean a larger number, since 10^-3 is bigger than 10^-5, and that the sign of the exponent describes size while the sign of the coefficient describes direction.
Precision
Coefficients are rounded to seven significant digits in the conversion mode and standard-form results to twelve. That is plenty for classroom and lab work but not for exact arithmetic with long digit strings. Addition and subtraction of scientific-notation values are not provided.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →