Write standard form
Objective. Express very large and small numbers in standard form.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
Standard form expresses a number as A × 10ⁿ, where A is between 1 and 10 and n is an integer showing how many places the decimal point has moved. For a large number, count how many places the decimal point moves left to reach a value between 1 and 10, and that count becomes a positive power of 10. For a small number less than 1, the decimal point moves right, giving a negative power of 10. For example, 47 000 becomes 4.7 × 10⁴, since the point moves four places left from 47000.0. Standard form makes very large or small numbers, such as the distance to the Sun or the mass of an atom, much easier to read and compare.
Worked example
Write the number 0.000382 in standard form.
- 1Move the decimal point right until one non-zero digit remains before it: 3.82.
- 2Count how many places the point moved: 4 places.
- 3Since the original number is less than 1, the power of 10 is negative.
- 40.000382 = 3.82 × 10⁻⁴.
Answer: 3.82 × 10⁻⁴
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes leave the coefficient outside the range 1–10, writing 47 000 as 47 × 10³ instead of 4.7 × 10⁴. Always check that the first factor is between 1 and 10.
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