GCSE — mathsFoundation2 min read

Standard Form (Scientific Notation)

Write and calculate with numbers in standard form for GCSE Maths. Convert between standard form and ordinary numbers.

Tutor AI Team2026-02-25T01:42:18.587Z

Standard form (scientific notation) is a way of writing very large or very small numbers compactly. It's used extensively in science and engineering, and is a key GCSE topic.

Core Concepts

The Format

$A \times 10^n$

where $1 \leq A < 10$ and $n$ is an integer.

Large Numbers (Positive Power)

$5,400,000 = 5.4 \times 10^6$

Count: the decimal point moves 6 places left.

Small Numbers (Negative Power)

$0.00032 = 3.2 \times 10^{-4}$

Count: the decimal point moves 4 places right.

Converting to Ordinary Numbers

$7.1 \times 10^5 = 710,000$

$2.5 \times 10^{-3} = 0.0025$

Calculations in Standard Form

Multiplication

$(3 \times 10^4) \times (2 \times 10^3) = 6 \times 10^7$

Multiply the numbers, add the powers.

Division

$(8 \times 10^6) \div (4 \times 10^2) = 2 \times 10^4$

Divide the numbers, subtract the powers.

Addition/Subtraction

Make the powers the same first, then add/subtract.

$(3.5 \times 10^4) + (2.1 \times 10^3) = (3.5 \times 10^4) + (0.21 \times 10^4) = 3.71 \times 10^4$

Worked Example: Write in Standard Form

Problem

$0.00056 = 5.6 \times 10^{-4}$

Solution

Worked Example: Calculate

Problem

$(4.2 \times 10^3) \times (3 \times 10^5) = 12.6 \times 10^8 = 1.26 \times 10^9$

(Adjust: $12.6 = 1.26 \times 10^1$ , so add 1 to the power.)

Solution

Common Mistakes

$A$ not between 1 and 10. $34 \times 10^5$ is not standard form; it should be $3.4 \times 10^6$ .
Wrong sign on the power. Large numbers → positive power. Small numbers → negative power.
Not adjusting after calculations. If $A \geq 10$ , divide by 10 and increase the power by 1.

Practice Problems

1. Write $72,000$ in standard form.
1. Write $0.0091$ in standard form.
1. Calculate $(5 \times 10^3) \times (4 \times 10^{-2})$ .
1. Calculate $(9 \times 10^7) \div (3 \times 10^4)$ .
1. Order: $3.2 \times 10^5$ , $4.1 \times 10^4$ , $8 \times 10^5$ .

Want to check your answers and get step-by-step solutions?

Key Takeaways

✓
Standard form: $A \times 10^n$ where $1 \leq A < 10$ .
✓
Positive power = large number. Negative power = small number.
✓
Multiply: multiply $A$ values, add powers. Divide: divide, subtract powers.
✓
Always check that $A$ is between 1 and 10 after calculations.

Tags:

#gcse#maths#number#standard-form#scientific-notation

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