Scientific notation

Steps

1. Move the decimal point until the number is between 1 and 10.
2. Count the moves: moving left gives a positive power of 10; moving right gives a negative one.
3. When multiplying, multiply the numbers and add the powers; then fix the first part to be between 1 and 10.

Worked examples

numbers: 3 × 4     = 12
powers:  10⁵ × 10⁻² = 10³
12 × 10³ = 1.2 × 10¹ × 10³ = 1.2 × 10⁴     first part must be between 1 and 10

0.000 304   → 3.04       point moves 4 places right → 3.04 × 10⁻⁴
56 000 000  → 5.6        point moves 7 places left  → 5.6 × 10⁷

For the whole topic, read Indices and scientific notation: key points, common mistakes and how the DSE tests it.

Other methods in this topic