™
Back
Standard form
Years 9 to 11
Standard form writes very big or very small numbers as a number between 1 and 10 times a power of ten.
For learners
Scientists work with huge and tiny numbers. Standard form keeps them short.
To write 45 000 in standard form, move the decimal point until the number is between 1 and 10. That gives 4.5, and the point moved 4 places. So 45 000 = 4.5 × 10⁴.
Tiny numbers use a negative power. 0.003 = 3 × 10⁻³.
A worked example
Write 0.0072 in standard form.
- Move the point 3 places right to get 7.2.
- Moving right means a negative power.
- 0.0072 = 7.2 × 10⁻³.
For grown-ups
The first number must be at least 1 and less than 10. Count how many places the decimal point moved: that is the power. Big numbers have positive powers and numbers between 0 and 1 have negative powers. Calculators show standard form with an E, for example 4.5E4.
Common mistakes
- Writing 45 × 10³, which is not in standard form because 45 is more than 10.
- Using a positive power for a small number.
- Counting the wrong number of places.
Why it matters
The distance to the Sun, the size of an atom and the number of people on Earth are all written in standard form.
Topics in quarter that use this
- Standard form: first steps
- Standard form
- Numbers to a million
- Significant figures and estimating