Scientific Notation Converter
Convert between decimal and scientific notation
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Need a fast answer on converting between decimal and scientific notation? Scientific Notation Converter answers with the steps beside it. You supply Number to Scientific Notation; the answer follows at once. Scientific Notation displays each intermediate figure as well. Anyone comparing options in Math can use Scientific Notation to compare scenarios. No sign-up is needed for Scientific Notation. The math runs on your device. Scientific Notation is part of the Math collection on CalcProMaster, alongside scientific notation converter calculator, free online scientific notation converter and more. Keep Scientific Notation bookmarked for next time. Try Scientific Notation now and keep it handy.
What the defaults give
0.000123 becomes 1.23 × 10⁻⁴, written in code as 1.23e-4.
The coefficient sits between 1 and 10 and the exponent counts the decimal places moved — four to the right in this case, hence the negative sign.
The rule
Scientific notation writes a number as a × 10ⁿ, where a is at least 1 and less than 10, and n is an integer.
To convert, move the decimal point until exactly one non-zero digit sits to its left, and count the moves. Moving left gives a positive exponent; moving right gives a negative one.
Worked examples
0.000123 → 1.23 × 10⁻⁴
0.5 → 5 × 10⁻¹
123,000 → 1.23 × 10⁵
6,000,000 → 6 × 10⁶
0.000000045 → 4.5 × 10⁻⁸
Reading and writing it
The exponent is the order of magnitude, so it tells you the size of the number before you look at the digits: 10⁵ is hundreds of thousands, 10⁻⁸ is tens of billionths. Calculators and programming languages write the same value as 1.23e-4, where the e stands for "times ten to the power". Calculators may also show E, and both mean the same thing.
Arithmetic shortcut
- Multiply: multiply the coefficients and add the exponents. 2×10³ × 3×10⁴ = 6×10⁷.
- Divide: divide the coefficients and subtract the exponents. 6×10⁷ ÷ 2×10³ = 3×10⁴.
- Add or subtract: bring both to the same exponent first, then add the coefficients.
- Powers: raise the coefficient to the power and multiply the exponent by it.
Re-normalise afterwards if the coefficient leaves the 1–10 range: 12 × 10³ is correctly written as 1.2 × 10⁴.
The exponent does the work: 1.23 × 10⁻⁴ means move the decimal four places left, giving 0.000123. That is why the coefficient stays between 1 and 10 — it keeps the significant figures in one place and the scale in the exponent. Converting back is the same rule in reverse, and the common mistake is counting zeros rather than places, which is how 10⁻⁴ becomes 0.0000123.
Frequently Asked Questions
What is 0.000123 in scientific notation?
1.23 × 10⁻⁴. The decimal point moves four places right to put one digit before it, so the exponent is negative four.
What does e-4 mean?
Times ten to the power of negative four, the same as 10⁻⁴. It is how calculators and programming languages print scientific notation.
Why must the coefficient be between 1 and 10?
For a single standard form. Any number can be written many ways, so the convention fixes one digit before the decimal point.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then re-normalise if the result is outside 1–10.
Is 1.23 × 10⁻⁴ the same as 123 × 10⁻⁶?
Yes, they are equal, but only the first is in standard form because its coefficient is between 1 and 10.
How many significant figures does it keep?
As many as the coefficient shows. 1.23 × 10⁻⁴ has three, which matters when the number came from a measurement.
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