How scientific notation works
A number in scientific notation is a coefficient (at least 1 but less than 10) times a power of ten:
a × 10ⁿ where 1 ≤ |a| < 10
To convert, slide the decimal point until one non-zero digit is in front of it, and count the moves. 42,000 becomes 4.2 × 10⁴ (4 places left), and 0.00042 becomes 4.2 × 10⁻⁴ (4 places right).
The three formats
- Scientific: 4.2 × 10⁴ — coefficient between 1 and 10.
- E-notation: 4.2E4 — how calculators write it.
- Engineering: exponent is a multiple of 3, matching metric prefixes.
Why use it
Scientific notation makes huge and tiny numbers manageable — the speed of light (3 × 10⁸ m/s) or the mass of an electron (9.1 × 10⁻³¹ kg) are far easier to read and compare than long strings of zeros. The order of magnitude (the exponent) alone often tells you what you need.
Frequently asked questions
What is scientific notation?
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of 10. For example, 42,000 becomes 4.2 × 10⁴, and 0.00042 becomes 4.2 × 10⁻⁴. It is a compact way to write very large or very small numbers.
How do you convert a number to scientific notation?
Move the decimal point so one non-zero digit remains in front of it, and count how many places you moved. Moving left gives a positive exponent; moving right gives a negative one. 42,000 → move 4 places left → 4.2 × 10⁴. This calculator does it instantly.
What is E-notation?
E-notation is how calculators and computers display scientific notation, replacing "× 10^" with the letter E. So 4.2 × 10⁴ is written 4.2E4, and 4.2 × 10⁻⁴ is 4.2E-4. The value is identical — just a different format.
What is engineering notation?
Engineering notation is like scientific notation but the exponent is always a multiple of 3, lining up with metric prefixes (kilo, mega, milli, micro). So 0.00042 is 420 × 10⁻⁶, which matches "420 microunits." It keeps the coefficient between 1 and 1000.
Tip: You can paste a number already in E-notation (like 6.02e23) and the calculator will reformat it.