Sheet № 133 · Foundation + Higher · AQA · Edexcel · OCR
How to Write Numbers in Standard Form –
Writing numbers in standard form is a key Number topic at GCSE. You need to convert both very large and very small numbers into the form A x 10^n, where 1 ≤ A < 10 and n is an integer. This appears on Foundation and Higher papers.
§Key definitions
Question:
Write 72,000 in standard form.
Answer:
7.2 × 10⁴
Q1 (Foundation):
Write 3,400,000 in standard form.
Q2 (Foundation):
Write 0.0072 in standard form.
Q3 (Higher):
The distance from the Earth to the Sun is approximately 149,600,000 km. Write this in standard form.
§Formulas to memorise
Standard form: A × 10^n where 1 ≤ A < 10 and n is an integer
Positive n means a large number (≥ 10); negative n means a small number (< 1)
Worked example
Write 72,000 in standard form.
Working:
⚠ Common mistakes
- ✗Writing A outside the range 1 to 10. For example, 45 × 10³ is not in standard form because 45 ≥ 10. The correct form is 4.5 × 10⁴.
- ✗Getting the sign of n wrong. Large numbers have positive powers; small numbers (less than 1) have negative powers. Think: "big number = big positive power."
- ✗Miscounting the number of places the decimal point moves. Count carefully, especially with numbers that have many zeros.
✦ Exam tips
- →Always double-check that A is between 1 (inclusive) and 10 (exclusive).
- →Convert your answer back to an ordinary number to verify it matches the original.
- →On ordering questions, compare the powers of 10 first — a higher power means a larger number for positive values.