Scientific Notation Calculator – Convert & Compare

Scientific notation stores a number as a coefficient times a power of ten so leading and trailing zeros stop carrying meaning. Converting 45,000,000 moves the decimal 7 places left: 4.5×10⁷. Converting 0.00032 moves it 4 places right: 3.2×10⁻⁴. The calculator normalizes any input, including engineering notation like 45E6 and messy decimals like 602,200,000,000,000,000,000,000 → 6.022×10²³ (Avogadro). Arithmetic follows exponent rules: (2×10³)(4×10⁵) = 8×10⁸, and (6×10⁸)/(3×10⁻²) = 2×10¹⁰, with automatic re-normalization when the coefficient product leaves [1,10) — e.g. 4×4 = 16 becomes 1.6 and bumps the exponent. Addition aligns exponents first: 9.7×10⁵ + 3×10⁴ = 10×10⁵ = 1.0×10⁶.

1. 1

   Enter a number

   Any format works: plain decimals, E-notation like 4.5E7, or big integers

2. 2

   Normalize the coefficient

   Shift the decimal until 1 ≤ |a| < 10

3. 3

   Count the shifts

   Left moves give positive exponents; right moves give negative ones

4. 4

   Operate by exponent rules

   Add/subtract exponents on multiply/divide, then re-normalize

• 1

  Rightward decimal moves mean negative exponents: 0.001 = 1×10⁻³

• 2

  Multiplying adds exponents: 10³×10⁵ = 10⁸, coefficients multiply separately

• 3

  E-notation 4.5E7 is the same number as 4.5×10⁷

• Leaving the coefficient outside 1 ≤ |a| < 10, like 45×10⁶

• Adding exponents when the bases differ, e.g. 2³×5²

• Sign error on small numbers: 0.00032 = 3.2×10⁻⁴ not +4

• Forgetting to re-normalize 16×10⁵ into 1.6×10⁶