Number (all units) · Both
Standard Form & Indices
Writing numbers in standard form, calculating with standard form, and the laws of indices.
Standard form is used for very large or very small numbers. Index laws let you simplify powers quickly – essential for non-calculator work.
Standard form
A number in standard form is written as:
A × 10ⁿ
where 1 ≤ A < 10 and n is an integer.
Examples:
45,000 = 4.5 × 10⁴
0.0032 = 3.2 × 10⁻³
Worked example
Write 0.00056 in standard form.
Solution
Move the decimal point 4 places right: 5.6 **5.6 × 10⁻⁴**
Index laws
aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁰ = 1
a⁻ⁿ = 1/aⁿ
Worked example
Simplify: (3² × 3⁵) ÷ 3³
Solution
3² × 3⁵ = 3⁷ 3⁷ ÷ 3³ = 3⁴ = **81**
Practice questions
Try these without looking at the answers first.
Q1.Write 7,200,000 in standard form.
Show answer
7.2 × 10⁶
Q2.Write 0.000041 in standard form.
Show answer
4.1 × 10⁻⁵
Q3.Simplify: 5⁶ ÷ 5²
Show answer
5⁴ or 625