How to use the Scientific Notation
- Enter the number, however large or small.
- Set the significant figures you want to keep.
- Compare scientific and engineering forms.
- Use the expanded row when you need the plain decimal back.
How the calculation works
Scientific notation writes any value as a coefficient between 1 and 10 multiplied by a power of ten. It separates magnitude from precision: 0.00042 becomes 4.2 × 10⁻⁴, which makes it unambiguous that there are two significant figures — something the plain decimal cannot convey, since leading zeros are placeholders rather than measured digits.
Engineering notation restricts the exponent to multiples of three so it maps directly onto SI prefixes: kilo, mega, giga, milli, micro, nano. A value of 4.7 × 10⁻⁴ farads is awkward; 470 × 10⁻⁶ farads is 470 microfarads, which is what the component is actually labelled. Electronics and mechanical engineering default to this form for exactly that reason.
When multiplying values in scientific notation, multiply the coefficients and add the exponents; when dividing, divide and subtract. This keeps very large and very small quantities tractable by hand and is why the notation survives despite calculators handling the arithmetic anyway.
x = a × 10ⁿ with 1 ≤ |a| < 10 ; engineering form uses n as a multiple of 3Source: ISO 80000-1 on quantities and units; SI prefix conventions.
Worked example
Expressing a 0.000047 farad capacitor in a component list.
- Scientific: 4.7 × 10⁻⁵.
- Engineering: exponent must be a multiple of three, so use 10⁻⁶.
- Coefficient becomes 47.
47 × 10⁻⁶ F — a 47 µF capacitor, exactly as it is printed on the part.
Frequently asked questions
What is the difference between scientific and engineering notation?+
Scientific keeps the coefficient between 1 and 10; engineering forces the exponent to a multiple of three to match SI prefixes.
How do I multiply numbers in scientific notation?+
Multiply the coefficients, add the exponents, then renormalise the coefficient if it leaves the 1–10 range.
Do leading zeros count as significant?+
No. In 0.00042 only the 4 and 2 are significant, which scientific notation makes explicit.
What does e-4 mean on a calculator display?+
The same thing as × 10⁻⁴ — it is just a keyboard-friendly way of writing the exponent.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.