Standard index form

Adding and subtracting numbers in standard index form:

Convert them into ordinary numbers, do the calculation, then change them back if you want the answer in standard form.

Example 1

4.5 × 10⁴ + 6.45 × 10⁵

= 45,000 + 645,000

= 690,000

= 6.9 × 10⁵

Multiplying and dividing numbers in standard form:

Here you can use the rules for multiplying and dividing powers. Remember these rules:

• To multiply powers you add, eg, 10⁵ × 10³ = 10⁸
• To divide powers you subtract, eg, 10⁵ ÷ 10³ = 10²

Example 2

Simplify (2 × 10³) × (3 × 10⁶)

Solution

Multiply 2 by 3 and add the powers of 10:

(2 × 10³) × (3 × 10⁶) = 6 × 10⁹