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Scientific Notation Calculator & Converter

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Guide

Switch between the converter and the calculator at the top. Convert a number between decimal and scientific form, or do arithmetic on two numbers written in e-notation.

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Created by the Reeliy Editorial Team. Last updated: Oct 19, 2026

What is scientific notation?

Scientific notation writes a number as a significand multiplied by a power of ten. The significand is at least 1 and less than 10 in absolute value, and the exponent is a whole number that records how far the decimal point has moved.

N = a × 10n, with 1 ≤ |a| < 10 and n an integer

The form exists because very large and very small quantities are awkward in plain digits. The mass of an electron is about 0.00000000000000000000000000000091 kg, which is easy to misread; written as 9.1 × 10-31 kg it is compact and its size is obvious at a glance. The exponent tells you the order of magnitude, and the significand carries the meaningful digits.

E-notation

Calculators, spreadsheets and programming languages cannot print a raised exponent, so they use e-notation: the letter e stands for "times ten to the power of". The value 1.25 × 106 becomes 1.25e+6 and 4.5 × 10-4 becomes 4.5e-4. This e has nothing to do with Euler's number 2.71828; it is simply a separator between the significand and the exponent.

Engineering notation

Engineering notation is a close relative in which the exponent is always a multiple of three, so the significand may run from 1 up to 999.999. It lines up with SI prefixes such as kilo, mega and milli. For example 7.2 × 10-5 is written 72 × 10-6 in engineering form, which reads directly as 72 micro-units. This calculator produces the normalised scientific form, but you can shift the exponent to a multiple of three by hand.

Using this calculator

Choose Converter to change the representation of one number, or Calculator to combine two numbers.

  • Decimal to Scientific: type an ordinary number. You get the scientific form (a × 10n) and the e-notation form.
  • Scientific to Decimal: type the number in e-notation (for example 3.2e4) in the first field and leave the exponent empty, or type only the significand (3.2) and put the power of ten (4) in the exponent field. The answer is the plain decimal with thousands separators.
  • Calculator: enter two numbers, choose add, subtract, multiply or divide, and you receive the result in scientific form, e-notation and decimal form together.

Negative numbers and negative exponents are accepted. Zero has no normalised scientific form, because no power of ten can bring it into the range from 1 to 10, so the converter gives no result for it.

Converting between decimal and scientific notation

Conversion is nothing more than moving the decimal point and counting the steps.

Decimal to scientific

  1. Move the decimal point until exactly one non-zero digit sits to its left.
  2. Count the places you moved it. Moving left gives a positive exponent, moving right gives a negative one.
  3. Write the shifted number times 10 raised to that count.

Example: 4,560,000 needs the point moved six places to the left to become 4.56, so it equals 4.56 × 106. For 0.000072 the point moves five places to the right to give 7.2, so it equals 7.2 × 10-5.

The converter keeps up to six decimals in the significand and drops trailing zeros. So 123,456,789.123456789 is shown as 1.234568 × 108: the long tail of digits is rounded, and the e-notation line (1.234568e+8) carries the same rounded value.

Scientific to decimal

Do the reverse: shift the decimal point by the exponent, to the right when it is positive and to the left when it is negative, padding with zeros as needed.

Example: 3.2 × 104 becomes 32,000, and 7.5 × 10-3 becomes 0.0075. Large results get thousands separators, so 1.25e+6 is shown as 1,250,000.

Arithmetic with scientific numbers

The rules follow from the laws of exponents. Multiplication and division are the easy cases because the powers of ten combine on their own:

(a × 10m) × (b × 10n) = (a × b) × 10m+n

(a × 10m) ÷ (b × 10n) = (a ÷ b) × 10m−n

Example: (3 × 108) × (2.5 × 10-3) = 7.5 × 105, which is 750,000. And (6 × 108) ÷ (2 × 103) = 3 × 105.

Addition and subtraction need matching exponents first, because you can only add quantities measured in the same unit of ten. Rewrite one number so both use the larger exponent, then add the significands:

4.2 × 105 + 3.1 × 104 = 4.2 × 105 + 0.31 × 105 = 4.51 × 105

The same alignment applies to subtraction: 4.2 × 105 − 3.1 × 104 = 3.89 × 105. After any operation, renormalise so the significand is back between 1 and 10; a product of 12 × 103 becomes 1.2 × 104. The calculator mode does all of this for you and also lists the plain decimal result.

Precision and limits

Numbers are held as standard double-precision floating point values, which keep roughly 15 to 17 significant digits. Most decimals, such as 0.1 or 123.456, have no exact binary representation, and the decimal line of the results prints the stored value without hiding that. That is why 123.456 × 102 appears as 12,345.600000000000363797881 rather than 12,345.6: the trailing digits are the tiny binary rounding error, not a mistake in the arithmetic.

For measurements, keep only as many digits as your data justifies. Reading a long decimal tail as extra accuracy is a common error; the significant figures calculator shows how to round properly.

Division by zero is undefined and is reported as an error. Results beyond the range of double precision (roughly 10308) cannot be displayed.

Common mistakes

  • Reversing the sign of the exponent: numbers smaller than 1 have negative exponents, numbers of 10 or more have positive ones.
  • Leaving the significand outside the 1 to 10 range, as in 0.45 × 10-3. The value is right but the form is not normalised; write 4.5 × 10-4.
  • Adding the exponents when adding the numbers. Exponents add only in multiplication; in addition you must first align them.
  • Reading e as Euler's number. In 6.02e23 it means "times ten to the power of".

For further reading on related ideas, see the standard form calculator, the exponent calculator and the sum calculator. Unit prefixes are covered by the metric conversion tool.

Frequently asked questions

How do I write 0.0005 in scientific notation?

Move the decimal point four places to the right to get 5, then record the move as a negative exponent: 0.0005 = 5 × 10⁻⁴, or 5e-4 in e-notation.

What does the e in 3.4e+7 mean?

It stands for "times ten to the power of", so 3.4e+7 is 3.4 × 10⁷ = 34,000,000. It is not Euler's number.

Can scientific notation represent zero or negative numbers?

Negative numbers simply carry a minus sign on the significand, as in -1.5005 × 10³. Zero has no normalised form because no power of ten turns it into a number between 1 and 10, so the converter gives no result for it.

Why does the decimal result show strange trailing digits?

Computers store most decimals as the nearest binary fraction. The calculator prints that stored value in full, so a tiny rounding error such as ...000363797881 can appear after the digits you expected.

References

  1. NIST Special Publication 811, Guide for the Use of the International System of Units (SI)
  2. IEEE 754-2019, IEEE Standard for Floating-Point Arithmetic

Cite this calculator and page

If you use this page in your work, you can cite it as:

Reeliy Editorial Team. (2026). Scientific Notation Calculator & Converter. Reeliy. https://reeliy.com/calculators/scientific-notation-calculator“Scientific Notation Calculator & Converter.” Reeliy, 2026, https://reeliy.com/calculators/scientific-notation-calculator.