Convert a decimal number to scientific notation, or turn scientific notation back into a decimal. Enter a value such as 0.00072, 3450000, or 3.45e6. The calculator shows both forms and explains the decimal shift.
Convert your number
Exact decimal conversion, with no rounding. Up to 200 input digits and an input exponent from −1000 to 1000. This tool converts notation; it does not determine measurement precision or significant figures.
What is scientific notation?
Scientific notation writes a nonzero number as a × 10n, where the coefficient a has an absolute value of at least 1 and less than 10, and n is an integer. For example, 72,000 becomes 7.2 × 104. A negative number keeps its minus sign: −72,000 becomes −7.2 × 104.
The power of ten tells you how to recover the original value. A positive exponent makes the coefficient larger in magnitude; a negative exponent makes it smaller. The exponent does not determine whether the number itself is positive or negative.
How to convert a decimal to scientific notation
- Find the first nonzero digit. Place the decimal point immediately after it, keeping the remaining digits in their original order.
- Count the decimal places moved. Moving the point to the left gives a positive exponent. Moving it to the right gives a negative exponent.
- Check the value. Multiplying the coefficient by the chosen power of ten must give the number you started with.
For 0.00072, move the decimal point four places to the right to get 7.2. To compensate, multiply by 10−4: 0.00072 = 7.2 × 10−4.
For 3,450,000, move it six places to the left: 3,450,000 = 3.45 × 106. Commas make that example easier to read, but omit them when entering numbers in the calculator.
Scientific notation examples
| Decimal | Scientific notation | E notation |
|---|---|---|
| 3,450,000 | 3.45 × 106 | 3.45e6 |
| 0.00072 | 7.2 × 10−4 | 7.2e−4 |
| −980,000 | −9.8 × 105 | −9.8e5 |
| 5 | 5 × 100 | 5e0 |
How to convert scientific notation to a decimal
Start with the coefficient and move the decimal point by the exponent’s number of places. Move right for a positive exponent and left for a negative exponent, adding zeros where needed.
For example, 6.25 × 10−3 = 0.00625. Conversely, 6.25 × 103 = 6250. With an exponent of zero, the value stays 6.25 because 100 = 1.
What does E mean?
In this context, E means “times ten to the power of.” The input 3.45e6 is another way to write 3.45 × 106. It is not multiplication by Euler’s number e. You may use uppercase E or lowercase e in the calculator.
Precision, trailing zeros, and zero
This calculator rearranges decimal digits without rounding. It can therefore convert values such as 9007199254740993 without losing the final digit. It accepts up to 200 digits, with an input exponent from −1000 to 1000.
It does not infer significant figures. For instance, 1.200 and 1.2 have the same numerical value, but they can express different measurement precision. The converter may omit trailing zeros; retain them separately when your measurement requires them.
Zero is a special case: it has no normalized coefficient with an absolute value between 1 and 10. The calculator displays 0 × 100 as a convenient convention.