Calculate the coefficient and scale

1 · Learn

Multiply standard-form numbers by multiplying coefficients and adding powers of ten, then normalise the coefficient. Division divides coefficients and subtracts exponents. Addition first needs matching powers.

Check magnitude with an estimate. A coefficient outside the interval from 1 up to but not including 10 needs an adjusted exponent.

2 · Worked example

(3 × 10⁴)(4 × 10³) = 12 × 10⁷ = 1.2 × 10⁸.

3 · Your turn

Calculate (6 × 10⁵) / (2 × 10²).

4 · Apply your learning

Explain why 3 × 10⁴ + 4 × 10³ equals 3.4 × 10⁴, not 7 × 10⁷.