What is Standard Form?

A number written as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

Formula: a × 10ⁿ (1 ≤ a < 10)

Example: 3500 = 3.5 × 10³ 0.006 = 6 × 10⁻³

Large Numbers

Count how many places the decimal point moves to the LEFT. This is your positive power.

Example: 45000 → 4.5 × 10⁴

Small Numbers

Count how many places the decimal point moves to the RIGHT. This is your negative power.

Example: 0.0032 → 3.2 × 10⁻³

The Rule of A

The leading number MUST be between 1 and 10. 12 × 10³ is NOT in standard form.

Comparing Sizes

First compare the powers of 10. If the powers are the same, compare the leading numbers.

Example: 2 × 10⁵ > 9 × 10⁴ because 10⁵ is larger than 10⁴.

Multiplication

Multiply the numbers and add the powers of 10.

Formula: (A × 10ᵃ) × (B × 10ᵇ) = (A×B) × 10ᵃ⁺ᵇ

Example: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷

Division

Divide the numbers and subtract the powers of 10.

Formula: (A × 10ᵃ) ÷ (B × 10ᵇ) = (A/B) × 10ᵃ⁻ᵇ

Example: (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴

Addition & Subtraction

Convert both numbers to the SAME power of 10 before adding or subtracting.

Example: (3 × 10⁴) + (5 × 10³) = (30 × 10³) + (5 × 10³) = 35 × 10³ = 3.5 × 10⁴

Adjusting the Answer

If your calculation result isn't between 1 and 10, shift the decimal and adjust the power.

Example: 20 × 10⁵ = 2 × 10⁶

Negative Powers in Division

Be careful: subtracting a negative power means ADDING.

Example: 10⁵ ÷ 10⁻³ = 10⁸

Standard Form on Calcs

Use the ×10ˣ or EXP button. Be careful with brackets during division!