Scientific Notation Converter
Scientific notation expresses any number as a coefficient (a) multiplied by a power of ten (10ᵇ), where 1 ≤ |a| < 10 and b is an integer. This compact form is indispensable in science and engineering for representing extremely large numbers like the speed of light (3 × 10⁸ m/s) or tiny quantities like the mass of an electron (9.11 × 10⁻³¹ kg) without writing out endless zeros.
Engineering notation is a variant that restricts the exponent to multiples of three, aligning with SI prefixes such as kilo (10³), mega (10⁶), and nano (10⁻⁹). This converter works bidirectionally: enter a decimal number to get both scientific and engineering forms, or enter a coefficient and exponent to recover the full decimal value.
How it works
N = a × 10ᵇ, where 1 ≤ |a| < 10 and b is an integer. Engineering notation uses b as a multiple of 3. To convert: b = floor(log₁₀|N|), a = N / 10ᵇ.
Use cases
- Expressing astronomical distances such as light-years or parsecs
- Writing atomic and subatomic measurements in physics and chemistry
- Reading and interpreting scientific paper data and constants
- Simplifying very large or very small numbers for engineering calculations
- Converting between engineering prefixes (kilo, mega, giga, micro, nano)
Frequently asked questions
How do you convert a number to scientific notation?
Move the decimal point until exactly one nonzero digit remains to its left, then count how many places you moved it — that count becomes the exponent of 10. For example, 4500 becomes 4.5 × 10³ because the decimal moved three places left. Mathematically, the exponent is b = floor(log₁₀|N|) and the coefficient is a = N / 10ᵇ.
What is the difference between scientific and engineering notation?
Scientific notation allows any integer exponent and keeps the coefficient between 1 and 10, while engineering notation restricts the exponent to multiples of three. Engineering notation aligns directly with SI prefixes such as kilo (10³), mega (10⁶), and nano (10⁻⁹), which makes it more practical for reading electrical and mechanical measurements.
How do you convert scientific notation back to a decimal number?
Multiply the coefficient by the power of ten: a positive exponent moves the decimal point that many places to the right, and a negative exponent moves it to the left. For example, 3 × 10⁸ expands to 300,000,000. This converter performs the expansion automatically when you enter a coefficient and exponent.
What does a negative exponent mean in scientific notation?
A negative exponent indicates a number smaller than 1, since 10⁻ᵇ equals 1 divided by 10ᵇ. For instance, 10⁻³ equals 0.001, and the mass of an electron is written as 9.11 × 10⁻³¹ kg. The larger the negative exponent, the smaller the quantity being represented.
Why must the coefficient be between 1 and 10?
Requiring 1 ≤ |a| < 10 gives every number exactly one normalized representation, which avoids ambiguity like writing the same value as 45 × 10² or 0.45 × 10⁴. It also makes comparing magnitudes easy: you can rank numbers just by looking at their exponents, then compare coefficients when the exponents match.