Free Standard Form Calculator with Steps
Convert between standard form and ordinary numbers with step-by-step working. Multiply, divide, add and subtract. Perfect for GCSE and A-Level maths exams.
Enter any number to convert to standard form (A × 10ⁿ)
Key Formulas
A × 10ⁿ where 1 ≤ |A| < 10
A is the coefficient (between 1 and 10), n is the integer exponent.
(a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10ᵐ⁺ⁿ
Multiply coefficients, ADD exponents.
(a × 10ᵐ) ÷ (b × 10ⁿ) = (a ÷ b) × 10ᵐ⁻ⁿ
Divide coefficients, SUBTRACT exponents.
Common Mistakes
Wrong coefficient range
Always check: Is A between 1 and 10?
Wrong sign on exponent
Small numbers (< 1) have NEGATIVE exponents. Large numbers (≥ 10) have POSITIVE exponents.
What is Standard Form?
Standard form (also called scientific notation in the US) is a way of writing very large or very small numbers using powers of 10.
In GCSE maths, standard form questions appear in the "Number" unit and are worth 2-4 marks. You need to know how to convert between standard form and ordinary numbers, and perform calculations.
Standard Form Format
A × 10ⁿ
Key Rules for GCSE
Large Numbers (≥ 10)
Move decimal LEFT → POSITIVE exponent
45,000 = 4.5 × 10⁴
3,200,000 = 3.2 × 10⁶
Small Numbers (< 1)
Move decimal RIGHT → NEGATIVE exponent
0.0032 = 3.2 × 10⁻³
0.00007 = 7 × 10⁻⁵
Multiplying & Dividing
Multiply:
ADD exponents
Divide:
SUBTRACT exponents
💡 Exam Tip
Always check your coefficient is between 1 and 10. If you get 12 × 10⁵, adjust to 1.2 × 10⁶ by moving the decimal and adding 1 to the exponent.
Worked Examples
Example 1: Convert 5,600,000
Step 1: Move decimal to get 5.6
5,600,000 → 5.6 (moved 6 places left)
Step 2: Count moves = positive exponent
6 places left = 10⁶
Answer: 5.6 × 10⁶
Example 2: (4 × 10³) × (3 × 10⁵)
Step 1: Multiply coefficients
4 × 3 = 12
Step 2: Add exponents
10³ × 10⁵ = 10⁸
Step 3: Adjust (12 not between 1-10)
Answer: 1.2 × 10⁹
Frequently Asked Questions
What is standard form in maths?
Standard form is A × 10ⁿ where A is between 1 and 10, and n is an integer. It's used to write very large or small numbers compactly.
How do I know if the exponent is positive or negative?
Large numbers (≥10) have positive exponents. Small numbers (<1) have negative exponents. Remember: moved LEFT = positive, moved RIGHT = negative.
What's the difference between standard form and scientific notation?
They are the same thing! "Standard form" is the UK term used in GCSE exams. "Scientific notation" is the American term.
How do I multiply in standard form?
Multiply the coefficients (A values) and ADD the exponents. Then adjust if the new coefficient isn't between 1 and 10.
How do I add numbers in standard form?
Convert both to ordinary numbers first, add them together, then convert the answer back to standard form.
Is this calculator aligned with GCSE?
Yes! It covers the entire GCSE standard form topic for Edexcel, AQA, and OCR, showing the exact working expected in exam answers.
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