Scientific Notation Calculator

Use scientific notation whenever a number is too large or too small to write comfortably in standard form. It compresses values like 0.0000000000667 into 6.67e-11 and 299,792,458 into 2.99792458e+8, making them easier to read, compare, and carry through formulas without losing track of the scale.

A number is normalized when the mantissa falls in [1, 10) and is multiplied by an integer power of ten. So 12,300 becomes 1.23 x 10^4, not 12.3 x 10^3. That constraint makes the exponent unique, which is why normalized form is the standard for scientific and engineering work. This calculator always returns normalized results.

E-notation is the computer-friendly shorthand for scientific notation. The letter e reads as "times ten to the power of", so 1.23e+4 means 1.23 x 10^4 = 12,300 and 5e-3 means 5 x 10^-3 = 0.005. This calculator accepts e-notation as input and always displays results in e-notation form.

It aligns both values to the larger of the two exponents, then adds the scaled mantissas and renormalizes. For 1.2 x 10^3 + 3.4 x 10^2, the second term becomes 0.34 x 10^3, the mantissas sum to 1.54, and the result is 1.54 x 10^3. Aligning to the larger exponent preserves precision when the magnitudes are close.

Scientific notation makes significant figures unambiguous: every digit in the mantissa counts. Writing 4,500 as 4.5 x 10^3 signals two significant figures; writing it as 4.500 x 10^3 signals four. The exponent never contributes to the significant figure count. This calculator runs the arithmetic in full double precision and rounds the displayed mantissa to 10 decimal places.