Standard form
Standard form
- Standard form writes a number as $A \times 10^n$, with $1 \leq A < 10$ and $n$ an integer.
- Count how far the decimal point moves:
- $4\,500\,000 = 4.5 \times 10^6$ (point moves 6 left → positive power),
- $0.00072 = 7.2 \times 10^{-4}$ (point moves 4 right → negative power).
Practice
Write 4 500 000 as A × 10ⁿ. What is the power n?
4 500 000 = 4.5 × 10⁶, so n = 6.
Practice
Write 0.00072 in standard form A × 10ⁿ. What is n?
0.00072 = 7.2 × 10⁻⁴, so n = −4.
Calculating
- Multiply the front numbers and add the powers:
- $(3 \times 10^5) \times (2 \times 10^{-2}) = 6 \times 10^3$.
Practice
(3 × 10⁵) × (2 × 10⁻²) = A × 10³. What is A?
3 × 2 = 6 and 10⁵ × 10⁻² = 10³, so the answer is 6 × 10³.
You've got it
Key idea
- standard form $A \times 10^n$ with $1 \leq A < 10$
- big numbers → positive power; small (< 1) → negative power
- multiply: multiply the fronts, add the powers