Standard form: writing very large and small numbers

Standard form writes a positive number as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer. Positive powers represent large numbers; negative powers represent small numbers.

The idea

Move the decimal point until the first factor is at least 1 but less than 10. Count the places moved to find the power. Check the result by multiplying back. When multiplying numbers in standard form, multiply the first factors and add the powers, then adjust the result so that its first factor is in the required range.

Worked example

Write 0.00072 in standard form and calculate (3 × 10⁴)(4 × 10³).

0.00072 = 7.2 × 10⁻⁴: the negative power makes the value smaller than one.
(3 × 10⁴)(4 × 10³) = 12 × 10⁷.
Rewrite the product as 1.2 × 10⁸ to put it in standard form.

A mistake to avoid

12 × 10⁷ has the right value but is not in standard form, because 12 is not less than 10.

Check your understanding

Write 5,600,000 in standard form.

Show the explanation

5.6 × 10⁶.

Explore the lesson

This guide connects to Integers, Powers and Standard Form in the IGCSE Mathematics course. The first two published lessons per subject are free previews; further interactive lessons require an account.