- Scientific notation
- 1.23456789e+8
- Decimal form
- 123456789
How it works
Align powers before adding coefficients
3×10⁶ + 2×10⁵ equals 3.2×10⁶ because 2×10⁵ is 0.2×10⁶. Adding coefficients and exponents independently would mix the rules for addition and multiplication and produce a completely different magnitude.
Reading a number in scientific notation
Scientific notation separates a coefficient from a power of ten. A positive exponent moves the scale toward larger values, while a negative exponent represents a smaller magnitude. Use arithmetic mode when combining numbers already written this way. Check whether the displayed digits reflect the requested precision; changing the notation alone does not make a measurement more accurate.
Scientific notation: formula and assumptions
Scientific notation writes a number as a × 10ⁿ, with 1 ≤ |a| < 10.
For zero, the mantissa and exponent are both zero.
Scientific notation arithmetic: formula and assumptions
Operate on the decimal quantities, then normalize the coefficient and exponent.
Square and square root ignore the second field. Power requires a whole-number exponent within ±1,000.
Worked example
Using the Scientific notation example:
- Number
- 123456789
Scientific notation writes a number as a × 10ⁿ, with 1 ≤ |a| < 10.
Example result
Scientific notation: 1.23456789e+8
Decimal form: 123456789
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
What makes scientific notation normalized?
For a nonzero number, the coefficient's magnitude is at least 1 and below 10, with the scale represented by an integer power of ten.
Do square and square-root operations use both input values?
No. They use only the first value. Power uses a whole-number exponent within the mode's stated bounds.
Prepared by Finflo. See our methodology and editorial policy.