Sheet № 05 · Foundation + Higher · AQA · Edexcel · OCR
Standard Form –
Standard form — also called standard index form or scientific notation — is a compact way of writing very large or very small numbers. It appears on both Foundation and Higher GCSE Maths papers, typically in questions about space, biology, or physics contexts. You need to convert numbers into and out of standard form, and perform calculat
§Key definitions
Question:
Write 0.000047 in standard form.
Answer:
4.7 × 10⁻⁵
Q1 (Foundation):
Write 3,600,000 in standard form.
Q2 (Foundation):
Write 8.1 × 10⁻³ as an ordinary number.
Q3 (Higher):
Work out (6.4 × 10⁸) ÷ (1.6 × 10³). Give your answer in standard form.
§Formulas to memorise
A number in standard form is written as a × 10^n, where 1 ≤ a < 10 and n is an integer
For large numbers, n is positive. For example, 4,500,000 = 4.5 × 10⁶.
For small numbers, n is negative. For example, 0.00032 = 3.2 × 10⁻⁴.
Worked example
Write 0.000047 in standard form.
Working:
⚠ Common mistakes
- ✗Writing a value outside the range 1 ≤ a < 10. For example, writing 45 × 10³ instead of 4.5 × 10⁴. Examiners will not award the mark if a is not between 1 and 10.
- ✗Getting the sign of n wrong. Large numbers have positive powers; small numbers (less than 1) have negative powers. Double-check by asking: "Is this number big or tiny?"
- ✗Forgetting to adjust after multiplying or dividing. If multiplying the a values gives 24.8, you must write it as 2.48 × 10¹ and add 1 to the power.
- ✗Adding the powers when you should be adding the ordinary numbers. You cannot add standard form numbers by simply adding powers — you must convert to the same power of 10 or to ordinary numbers first.
✦ Exam tips
- →On non-calculator papers, break the multiplication into manageable parts. For example, 3.2 × 4.5 = 3 × 4.5 + 0.2 × 4.5 = 13.5 + 0.9 = 14.4.
- →Use standard form with other topics. You might see it in compound interest, area and volume, or probability questions. Recognise when an answer needs converting.
- →When comparing numbers in standard form, look at the power first. A larger power of 10 always means a larger number (for positive numbers). Only compare the a values when the powers are equal.
- →Remember the key formulas for multiplying and dividing — these are listed in our formulas guide.
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