What the Scientific Notation Converter does
This converter writes any number in scientific notation (standard form), engineering notation with its SI prefix, E notation and ordinary decimal form, and it adds, subtracts, multiplies and divides numbers given in any of those forms - keeping the right number of significant figures and showing the working step by step.
Numbers are handled as exact decimals rather than as computer floating point, so 0.1 × 0.2 gives exactly 0.02 and a 40-digit result keeps every digit. Significant figures are read from the way you write each number and the standard school rules decide the precision of the answer. It all runs in your browser; nothing is sent anywhere.
How to use it
- Choose Convert to rewrite one number, or the arithmetic option to combine two.
- Type the number the way you have it:
0.000456,4.56e-4,4.56E-4,4.56 x 10^-4or4.56×10⁻⁴all work, and so do thousands separators such as 1,234,567. - Leave significant figures on "As written" to keep the precision your numbers imply, or pick a number to round to.
- For arithmetic, choose the operation and type the second number. The answer is rounded by the significant-figure rules, and the exact result is listed underneath.
- Read the working - how far the decimal point moved, or how the mantissas and powers of ten were combined - and copy the result in scientific or E notation.
Reading the results
Scientific notation writes a number as a × 10^n, with a between 1 and 10. Engineering notation instead keeps n a multiple of three, so the mantissa can be 1 to 999 and maps onto SI prefixes: 4.7 × 10^4 ohms is 47 × 10^3, or 47 kΩ. E notation is the same as scientific notation written for keyboards: 4.7E+4.
A warning about trailing zeros means a whole number such as 1200 could have two, three or four significant figures. The calculator counts two and tells you; write 1.200 × 10^3 or 1200. to mean four.
Worked example: converting a constant and multiplying in standard form
The speed of light, 299,792,458 m/s: the decimal point moves 8 places to the left to leave one digit in front, so it is 2.99792458 × 10^8, or 2.99792458E+8 in E notation, with 9 significant figures. In engineering notation it is 299.792458 × 10^6 m/s (mega).
(6.02 × 10^23) × 2.5: multiply the mantissas, 6.02 × 2.5 = 15.05, and keep 10^23. Normalise to 1.505 × 10^24. The inputs have 3 and 2 significant figures, so the answer keeps 2: 1.5 × 10^24.
1.25 × 10^3 + 4.6 × 10^2 is 1,250 + 460 = 1,710. The first is precise to the tens and the second to the tens, so the answer is 1.71 × 10^3.
Formulas and scoring rules
- Scientific notation
x = a × 10^n, 1 ≤ |a| < 10, n = floor(log10 |x|)- Engineering notation
x = a × 10^(3k), 1 ≤ |a| < 100010^3 kilo, 10^6 mega, 10^9 giga, 10^-3 milli, 10^-6 micro, 10^-9 nano and so on.- Multiplying and dividing
(a × 10^m)(b × 10^n) = ab × 10^(m+n); (a × 10^m)/(b × 10^n) = (a/b) × 10^(m−n)Keep the smaller number of significant figures of the inputs.- Adding and subtracting
rewrite with the same power of ten, then add or subtract the mantissasKeep the least precise decimal place of the inputs.- Rounding
half away from zero: 2.45 to 2 s.f. = 2.5; −2.45 = −2.5Arithmetic is exact (integer arithmetic on the decimal digits); division is carried to over 40 digits before rounding.
Counting significant figures
Non-zero digits always count. Zeros between non-zero digits count (1.05 has three). Leading zeros never count (0.0045 has two). Trailing zeros count when there is a decimal point (4.500 has four, 120.0 has four) and are ambiguous in a whole number without one (1200). In scientific notation every digit of the mantissa counts, which is the main reason scientists use it: 1.20 × 10^3 says three significant figures unambiguously.
Limitations: what the result does not prove
- The significant-figure rules are a convention for reporting measured values. They are a simplified form of uncertainty analysis; for serious measurement work, propagate the actual uncertainties instead.
- Exact numbers - counts, defined constants, the 2 in a diameter = 2r - have unlimited significant figures. Type them with enough digits, or pick the significant figures you want, so they do not limit the answer.
- Very large exponents are accepted up to ±100,000, but decimal form is only written out up to 400 characters.
- Only one operation at a time. For longer expressions use the scientific calculator.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- BIPM - SI Brochure: SI prefixes
- NIST - Metric (SI) prefixes
- NIST SP 811 - Guide for the Use of the International System of Units (rounding and digits)
Frequently asked questions
How do I convert a number to scientific notation?
Move the decimal point until one non-zero digit is in front of it and count the places moved. That count is the power of ten - positive if you moved left, negative if you moved right. 0.000456 becomes 4.56 × 10^-4.
What is the difference between scientific and engineering notation?
Scientific notation keeps one digit before the decimal point. Engineering notation uses only powers of ten that are multiples of three, so the mantissa runs from 1 to 999 and matches SI prefixes such as kilo, mega, milli and micro.
What does E mean in a number like 3.2E+5?
E stands for “times ten to the power”. 3.2E+5 is 3.2 × 10^5 = 320,000 and 4.56E-4 is 0.000456. Calculators, spreadsheets and programming languages use it because a superscript is hard to type.
How do you multiply numbers in scientific notation?
Multiply the mantissas and add the exponents, then move the decimal point if the mantissa is 10 or more. (3 × 10^4)(2 × 10^-2) = 6 × 10^2. The answer keeps as many significant figures as the less precise input.
How do you add numbers written in standard form?
Rewrite them with the same power of ten, add the mantissas and normalise. 1.25 × 10^3 + 4.6 × 10^2 = 1.25 × 10^3 + 0.46 × 10^3 = 1.71 × 10^3. The answer is rounded to the least precise decimal place of the two.
How many significant figures does 1200 have?
It is ambiguous: two, three or four depending on whether the zeros were measured. This tool counts two and warns you. Writing 1.200 × 10^3, or 1200 with a decimal point, makes it four.
Last reviewed by the A2Z.Tools team against the sources listed above.
