By Charlotte Johnson
Updated August 30, 2022
Scientific notation represents numbers as a coefficient multiplied by a power of ten, making very large or very small values easier to handle. For example, 125 000 000 000 becomes 1.25 × 10¹¹; the exponent 11 indicates that moving the decimal point eleven places to the right restores the original value. When dividing such numbers, a simple set of rules yields an accurate result.
Express the problem in scientific form. For instance: 9 × 10⁸ ÷ 3 × 10⁵.
Divide the non‑power-of‑ten factors: 9 ÷ 3 = 3.
Subtract the exponent of the divisor from the exponent of the dividend: 8 – 5 = 3.
Multiply the quotient of the coefficients by the resulting power of ten: 3 × 10³.
Ensure the final coefficient lies between 1 and 10. If it falls below 1, adjust both the coefficient and exponent. For example, 0.3 × 10⁴ becomes 3 × 10³ after shifting the decimal one place to the right.
Divide the coefficients, subtract the exponents, then normalize the coefficient to the range 1–10.
