About the scientific notation calculator
Scientific notation writes very large or very small numbers as a coefficient between 1 and 10 multiplied by a power of ten. This calculator converts any number to scientific, E and engineering notation, and can add, subtract, multiply and divide numbers written in scientific notation.
Inputs can be plain decimals, E notation (3.45e-4) or the form 3.45x10^-4.
Who should use the scientific notation calculator
- Science and engineering students.
- Anyone working with very large or small measurements.
- Teachers demonstrating standard form.
How to use the scientific notation calculator: what each input means
- Operation
- Convert, add, subtract, multiply or divide.
- Number x and y
- Any decimal, E notation or ×10^ form.
How the scientific notation calculator works: method and formula
To convert, the decimal point is moved until one non-zero digit is before it, and the number of places moved becomes the exponent of 10. For multiplication, coefficients are multiplied and exponents added. For division, coefficients are divided and exponents subtracted. Addition and subtraction first align the exponents.
- Form
- a × 10^n with 1 ≤ |a| < 10
- Multiply
- (a × 10^m)(b × 10^n) = (ab) × 10^(m+n)
How to read your scientific notation calculator result
E notation is the same as scientific notation with e replacing × 10^. Engineering notation uses exponents that are multiples of three, which matches SI prefixes such as kilo, mega and milli.
Scientific Notation Calculator worked example
Convert 0.000345 and multiply it by 2.5e3.
- 0.000345 = 3.45 × 10^-4 (E notation 3.45e-4, engineering 345 × 10^-6).
- 0.000345 × 2500 = 0.8625, which is 8.625 × 10^-1.
0.000345 = 3.45 × 10^-4.
Practical uses of the scientific notation calculator
- Writing measurements for lab reports.
- Multiplying very large or small quantities.
- Converting E notation from a spreadsheet to standard form.
Assumptions and limitations of this calculator
- Inputs are limited to 500 significant digits.
- Division is rounded to 30 significant digits; other operations are exact.