Express very large or small numbers as mantissa times power of ten.
Overview
Scientific notation writes numbers as a × 10^k where 1 ≤ |a| < 10 and k is an integer exponent. It tames astronomy distances and atomic scales without long zero strings.
Converting moves the decimal point: 0.00072 becomes 7.2 × 10⁻⁴. Exponents add when multiplying powers of ten and subtract when dividing, while mantissas multiply or divide separately.
Calculators display SCI mode results; manual work requires normalizing mantissa after operations. Significant figures rules in science labs may limit reported digits in the mantissa.
Engineering notation uses exponents divisible by 3 (kilo, mega, milli) aligning with metric prefixes. Scientific notation is broader with any integer exponent.
Steps
Provide very large or small value.
Shift decimal to get 1 ≤ |a| < 10.
Count decimal moves for k.
Combine mantissas and exponents on multiply/divide.
Shift decimal using exponent sign.
Round mantissa per lab rules if needed.
Math
n = a × 10^k, 1 ≤ |a| < 10
Exponent k records how many places the decimal moved from n to normalized a.
Worked cases
Decimal moves 4 places right
7.2 × 10⁻⁴.
Mantissa 6, exponent 4+3
6 × 10⁷.
Normalize to 6.022 with exponent 23
6.022 × 10²³.
Why use this
Questions