What standard form is
- Standard form writes a number as A × 10ⁿ, where A is at least 1 and less than 10, and n is an integer.
- Large numbers have a positive power: 35 000 = 3.5 × 10⁴.
- Small numbers have a negative power: 0.0042 = 4.2 × 10⁻³.
Converting
- To write in standard form, place the decimal point after the first non-zero digit and count how many places it moved.
- To convert back, multiply by the power of 10: 6 × 10⁵ = 600 000 and 2.1 × 10⁻² = 0.021.
- 45 × 10³ is not in standard form because 45 is not between 1 and 10; it is 4.5 × 10⁴.
Multiplying and dividing
- Multiply the numbers and add the powers: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷.
- Divide the numbers and subtract the powers: (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴.
- If the number part is 10 or more, adjust: 20 × 10⁵ = 2 × 10⁶.
Adding and subtracting
- Convert to ordinary numbers (or the same power of 10) first: 4.5 × 10³ + 2 × 10² = 4500 + 200 = 4700 = 4.7 × 10³.
- On a calculator, use the ×10ˣ (or EXP) button.
Key terms
- Standard form
- A way of writing numbers as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer.
- Ordinary number
- A number written without powers of 10.
- Integer
- A whole number: positive, negative or zero.
- Power of 10
- A number such as 10³ = 1000 or 10⁻² = 0.01.