Standard Form Calculator

Convert Number to Standard Form

Convert Standard Form to Number

× 10^

Worked examples

Large number: 6,520,000 → the exponent is floor(log₁₀(6,520,000)) = 6, then coefficient = 6,520,000 / 10⁶ = 6.52. Result: 6.52 × 10⁶.

Small number: 0.000047 → the exponent is floor(log₁₀(0.000047)) = −5, then coefficient = 0.000047 / 10⁻⁵ = 4.7. Result: 4.7 × 10⁻⁵.

Reverse direction: coefficient 3.45, exponent 5 → 3.45 × 10⁵ = 345,000.

Why the exponent uses a floor of a logarithm

Standard form (scientific notation) requires the coefficient to fall between 1 and 10. Taking log₁₀ of the number and rounding down gives exactly the power of 10 needed to pull the coefficient into that range — this is the same reasoning that tells you a 7-digit number like 6,520,000 needs an exponent of 6, not 7, because the coefficient (6.52) must stay below 10.

Precision and formatting

Coefficients are rounded to 6 significant figures internally, then trailing zeros are stripped for display, so 5.000000 shows as 5, not 5.000000. Converting back to a plain number switches to exponential notation automatically once the result is ≥ 1,000,000 or < 0.0001, since printing something like 345,000,000,000 in full would be harder to read than 3.45 × 10¹¹.