Scientific Notation Converter
Convert a number to and from scientific notation.
Input sheet
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Scientific notation compresses very large or very small numbers into a tidy mantissa times a power of ten — the standard way to write distances in space, sizes of atoms, or populations.
How it works
Writes the number as a mantissa between 1 and 10 times a power of ten, found from the base-10 logarithm.
A number is written as a mantissa between 1 and 10 multiplied by a power of ten. The exponent is found from the base-10 logarithm: it is how many places the decimal point shifts. Positive exponents mean large numbers, negative ones mean small fractions.
This tool reports the mantissa, the exponent, and the original standard form, so you can move confidently in either direction.
Number = mantissa × 10^exponent, where the mantissa is between 1 and 10
Worked examples
Writing 0.00042 in scientific notation. → 4.2 × 10⁻⁴
The decimal moves four places right to get 4.2, so the exponent is −4.
Writing 93,000,000 (miles to the sun). → 9.3 × 10⁷
The decimal moves seven places left to leave 9.3, giving an exponent of 7.
Tips & gotchas
- A positive exponent counts how many places the decimal moves right (big numbers); a negative exponent moves it left (small numbers).
- The mantissa should always be at least 1 and less than 10 — that is what makes the notation 'normalized.'
- To multiply numbers in scientific notation, multiply the mantissas and add the exponents.
FAQ
What counts as a valid mantissa?
A value of 1 or more but less than 10. Normalized scientific notation always keeps a single nonzero digit before the decimal point.
What does a negative exponent indicate?
A number smaller than 1. Each unit of negative exponent shifts the decimal one place to the left, so 10⁻³ is one thousandth.
How is scientific notation different from engineering notation?
Engineering notation restricts exponents to multiples of three so they align with metric prefixes like kilo, mega, and milli; scientific notation allows any exponent.
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