GCSE Maths → Number → Standard Form
Standard Form GCSE Maths
Standard form is a way of writing very large and very small numbers using powers of 10. It is common in GCSE maths, science, engineering, and calculator-based exam questions.
This topic becomes much easier when students understand what the power of 10 is doing to the decimal point.
Video explanation
A short Worthing Maths Tutor video explanation for standard form GCSE maths can be embedded here later to improve student engagement and time on page.
What is standard form?
A number is in standard form when it is written like this:
where A is at least 1 but less than 10, and n is an integer.
This is in standard form because 4.7 is between 1 and 10.
Converting large numbers into standard form
For large numbers, move the decimal point until the first number is between 1 and 10. The number of places moved becomes the positive power of 10.
Example 1: Write 4200 in standard form
Move the decimal point 3 places left.
Example 2: Write 680000 in standard form
Move the decimal point 5 places left.
Converting small numbers into standard form
For small decimals, move the decimal point to the right until the first number is between 1 and 10. The power of 10 will be negative.
Example 3: Write 0.035 in standard form
Move the decimal point 2 places right.
Example 4: Write 0.00072 in standard form
Move the decimal point 4 places right.
Converting standard form back to ordinary numbers
A positive power moves the decimal point to the right. A negative power moves it to the left.
Example 5: Convert 6.1 × 10⁴ to an ordinary number
Move the decimal point 4 places right.
Example 6: Convert 8.3 × 10⁻³ to an ordinary number
Move the decimal point 3 places left.
Multiplying numbers in standard form
Multiply the front numbers, then multiply the powers of 10 by adding the indices.
Example 7: Multiply standard form numbers
Multiply the front numbers:
Add the powers:
So:
Dividing numbers in standard form
Divide the front numbers, then subtract the powers of 10.
Example 8: Divide standard form numbers
Divide the front numbers:
Subtract the powers:
So:
Common mistakes in standard form
- Using a first number that is not between 1 and 10.
- Forgetting that small decimals use negative powers.
- Moving the decimal point the wrong way.
- Adding powers when dividing instead of subtracting them.
- Leaving an answer like 12 × 10³ instead of changing it to 1.2 × 10⁴.
Practice questions
- Write 5300 in standard form.
- Write 720000 in standard form.
- Write 0.064 in standard form.
- Write 0.00091 in standard form.
- Convert 4.8 × 10³ to an ordinary number.
- Convert 6.2 × 10⁻² to an ordinary number.
- Calculate (2 × 10³)(4 × 10²).
- Calculate (9 × 10⁵) ÷ (3 × 10²).
Answers
- 5.3 × 10³
- 7.2 × 10⁵
- 6.4 × 10⁻²
- 9.1 × 10⁻⁴
- 4800
- 0.062
- 8 × 10⁵
- 3 × 10³
Standard form FAQ
What is standard form?
Standard form writes very large or very small numbers as a number between 1 and 10 multiplied by a power of 10.
What does a positive power of 10 mean in standard form?
A positive power of 10 usually represents a large number, such as 4.2 × 10³ = 4200.
What does a negative power of 10 mean in standard form?
A negative power of 10 usually represents a small decimal, such as 3.5 × 10⁻² = 0.035.
Is standard form on GCSE maths?
Yes. Standard form appears on GCSE maths papers, often in calculator questions, science-style contexts, and questions involving very large or very small numbers.
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