Standard Form

Overview

Standard form (also called standard index form) is a compact way of writing very large numbers using powers of 10. A number in standard form looks like A × 10ⁿ, where A is at least 1 but less than 10. In Year 8 students learn to write large numbers such as 4 500 000 as 4.5 × 10⁶ and to convert back again. It makes huge quantities — distances in space, populations, file sizes — far easier to read and compare.

What You Will Learn

• Understand that a number in standard form is written as A × 10ⁿ with 1 ≤ A < 10
• Write large whole numbers in standard form
• Convert a number from standard form back into an ordinary number
• Multiply and divide whole numbers and decimals by powers of 10
• Compare and order large numbers written in standard form

Key Vocabulary

Common Mistakes to Avoid

• Writing the first part A as 10 or more, e.g. 45 × 10⁵ instead of 4.5 × 10⁶
• Miscounting the number of places the digits move, giving the wrong power of 10
• Forgetting that A must be at least 1, e.g. writing 0.45 × 10⁷
• Treating the index as the number of zeros rather than the number of place-value shifts

Frequently Asked Questions