# Standard form

A short way to write very big or very small numbers as a number between 1 and 10 times a power of 10.

Maths (school) · Part 01: Number and ratio · Card 8 of 9 · Last updated 2026-10-19

## Analogy

Like writing 'one million' instead of counting every zero.

## Example

**Two conversions**

45,000 = 4.5 x 10^4
0.00032 = 3.2 x 10^-4

## In practice

Scientists use it for the distance to the Sun or the width of a cell.

## Practice

### Flashcards

- **Write 45,000 in standard form.** 4.5 x 10^4.

## Questions people ask

### How do you write a small number in standard form?

Move the decimal point right until the number is between 1 and 10, then count the moves. The count becomes a negative power of 10. For 0.00032, you move four places to get 3.2, so it is 3.2 x 10^-4.

### Why must the first number be between 1 and 10?

The rule keeps every number written the same way, so they are easy to compare. 4.5 x 10^4 is standard form, but 45 x 10^3 is not, even though both equal 45,000. Only one form of each number counts as standard.

## Related concepts

- [Laws of indices](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-7)
- [BIDMAS](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-1)
- [Adding fractions](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-2)
- [Percentage of an amount](https://studyvisually.com/learn/science/maths-school/maths-school-part-1/maths-school-part-1-concept-3)

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