Number sense
Scientific Notation: Large and Small Numbers Clearly
Updated October 2, 2026
Published by SolveCalc (Operator of solvecalc.live)
Scientific notation writes a number as m × 10n, where m is usually between 1 and 10 (not including 10), and n is an integer. It keeps very large or very small values readable.
Reading a number in scientific notation
| Scientific notation | Ordinary form |
|---|---|
| 3.5 × 10³ | 3,500 |
| 6.02 × 10²³ | 602,000,000,000,000,000,000,000 |
| 4.5 × 10⁻³ | 0.0045 |
| 1.2246 × 10⁻¹⁶ | 0.00000000000000012246 |
Positive exponents move the decimal point right. Negative exponents move it left.
Writing a number in scientific notation
- Move the decimal so one non-zero digit sits to the left of the point.
- Count how many places you moved—that count is |n|.
- If you moved left, n is positive. If you moved right, n is negative.
Example: 45,000 → move 4 places left → 4.5 × 10⁴. Example: 0.0071 → move 3 places right → 7.1 × 10⁻³.
Calculator e-notation
Many calculators show 1.5e3 for 1.5 × 10³ and 4.5e-3 for 4.5 × 10⁻³. Same idea, compact display.
Multiply and divide powers of ten
- Multiply: multiply the leading parts, add the exponents.
- Divide: divide the leading parts, subtract the exponents.
Example: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. Example: (8 × 10⁵) ÷ (2 × 10²) = 4 × 10³.
Practice on CalcSolver
Enter powers with ^ on the scientific calculator. For key layouts and log/ln, see How to use a scientific calculator.