How it works

Standard form writes numbers as a × 10^n, where 1 ≤ a < 10 and n is an integer. Large numbers have a positive power of 10 and small numbers (less than 1) have a negative power. When multiplying or dividing standard form numbers, combine the powers of 10 and the coefficients separately, then convert back to standard form if needed.

The method

1. 1.Move the decimal point until only one non-zero digit is before it
2. 2.Count how many places the decimal point moved to find n
3. 3.Use a positive power for numbers ≥ 1 and negative for numbers < 1
4. 4.Write in the form a × 10^n

Worked example

Write 45,000 in standard form.

1. Move decimal point 4 places: 4.5
2. 45000 = 4.5 × 10^4

Worked example

Write 0.00032 in standard form.

1. Move decimal point 4 places right: 3.2
2. 0.00032 = 3.2 × 10^-4

Common mistakes

• Writing the coefficient outside the range 1 ≤ a < 10
• Using the wrong sign on the power of 10 for small numbers
• Forgetting to adjust the power of 10 after multiplying coefficients