Scientific Notation Converter
Convert any number to and from scientific notation, e-notation, engineering notation, order of magnitude, and word form — with the decimal-point steps.
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Converting to scientific notation
Scientific notation writes a number as a mantissa between 1 and 10 times a power of ten. It makes very large and very small numbers easy to read and compare.
The steps
- Move the decimal point until exactly one non-zero digit is to its left.
- Count the places you moved it.
- The count is the exponent — positive if you moved left, negative if you moved right.
Tip: Moving the point left makes the exponent positive (a big number); moving it right makes it negative (a small number).
Worked examples
- 357096 → move 5 places left → 3.57096 × 10⁵.
- 0.005600 → move 3 places right → 5.600 × 10⁻³ (the trailing zeros stay).
- 124.7 → 1.247 × 10².
- 345600000000 → 3.456 × 10¹¹, engineering 345.6 × 10⁹, order of magnitude 11.
Converting back
Read the exponent and move the point the other way, filling zeros:
- 3.456e4 → 34560
- 3.456e-4 → 0.0003456
More forms
Alongside scientific notation, this converter shows e-notation, engineering notation (exponent a multiple of 3, matching kilo, mega, giga), the order of magnitude, and the number in words.
Common mistakes
- Moving the point the wrong way and flipping the exponent sign.
- Dropping significant trailing zeros from the mantissa.
- Leaving a mantissa of 10 or more instead of normalizing.
For the British term, see the standard form calculator, and to do arithmetic in scientific notation use the scientific notation operations calculator.
Frequently asked questions
- How do you convert a number to scientific notation?
- Move the decimal point until one non-zero digit is to its left, count how many places you moved, and use that count as the exponent. Moving left gives a positive exponent, moving right gives a negative one. So 357096 becomes 3.57096 times 10 to the 5th.
- How do you convert scientific notation back to a plain number?
- Move the decimal point by the exponent — right for a positive exponent, left for a negative one — filling in zeros as needed. So 3.456 times 10 to the 4th becomes 34560, and 3.456 times 10 to the negative 4th becomes 0.0003456.
- Are trailing zeros kept in scientific notation?
- Yes, when they follow the decimal point in the mantissa, because they are significant. 0.005600 becomes 5.600 times 10 to the negative 3rd, keeping both trailing zeros.
- What is engineering notation?
- Engineering notation is scientific notation with the exponent restricted to a multiple of 3, so it lines up with metric prefixes. 357096 is 357.096 times 10 to the 3rd, matching the kilo prefix.
- What is order of magnitude?
- The order of magnitude is the exponent in scientific notation — a rough measure of size in powers of ten. 345600000000 has an order of magnitude of 11.
- What is e-notation?
- E-notation replaces the times ten to the power part with the letter e, so 3.57096 times 10 to the 5th is written 3.57096e5. Calculators and programming languages use it.
- How is this different from the standard form calculator?
- They do the same conversion. Standard form is the British name for scientific notation, so use whichever term matches your textbook. This converter also adds engineering notation and word form.