Convert numbers to/from scientific notation and multiply or divide numbers in scientific notation with step-by-step work
a × 10ⁿ where 1 ≤ |a| < 10
A number is in proper scientific notation when the coefficient a satisfies 1 ≤ |a| < 10 and n is an integer exponent on 10.
Converting from standard form:
Moving the decimal point left → exponent is positive. (93,000,000 → 9.3 × 10⁷, decimal moved left 7 places)
Moving the decimal point right → exponent is negative. (0.000045 → 4.5 × 10⁻⁵, decimal moved right 5 places)
(a₁ × 10^n₁) × (a₂ × 10^n₂) = (a₁·a₂) × 10^(n₁+n₂)
(a₁ × 10^n₁) ÷ (a₂ × 10^n₂) = (a₁÷a₂) × 10^(n₁−n₂)
Multiply: multiply the coefficients and add the exponents.
Divide: divide the coefficients and subtract the exponents.
Always normalize: if the resulting coefficient is ≥ 10 or < 1, adjust it back to the range [1, 10) by shifting the coefficient and updating the exponent.
One-on-one Algebra 1 tutoring makes scientific notation, exponent rules, and all the big-number skills click — we work through your exact problems and build confidence for tests.