Standard form (scientific notation) — KCSE Mathematics

KCSE Mathematics · 83 practice questions · 4 syllabus objectives

37 easy37 medium9 hard

What You'll Learn

Key learning outcomes for this topic, aligned to the KNEC KCSE syllabus.

Write very large and very small numbers in standard form (A × 10ⁿ, where 1 ≤ A < 10 and n is an integer)

Perform addition, subtraction, multiplication and division on numbers expressed in standard form

Apply standard form to express measurements in science and engineering contexts (e.g. mass of electron, distance to stars)

Standard form (scientific notation)

Sample Questions

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1
easySHORT ANSWER2 marks

A small electronic device has a mass of 4.5 × 10⁻³ kg. Express this mass in grams using standard form. (2 marks)

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Part (a) — 2 marks
Convert kg to grams: 4.5 × 10⁻³ kg = 4.5 × 10⁻³ × 10³ g (1 mk)
Final answer: 4.5 g = 4.5 × 10⁰ g (in standard form) (1 mk)
2
easySHORT ANSWER3 marks

Identify the product of (3 × 10²) and (5 × 10⁴). Express your answer in standard form. (3 marks)

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Part (a) — 1 mark
Multiply the coefficients: 3 × 5 (1 mk)
Part (b) — 2 marks
Add the exponents: 2 + 4 (1 mk)
Combine results to express final answer in standard form (1 mk)
3
easySHORT ANSWER4 marks

Express the following numbers in standard form: (a) 4500000 [2 marks] (b) 0.000032 [2 marks].

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Part (a) — 2 marks
Correctly expressed as 4.5 × 10^6 (2 mks)
Part (b) — 2 marks
Correctly expressed as 3.2 × 10^(-5) (2 mks)
4

A scientist measures the mass of a dust particle as 3.2 × 10^(-7) kg. Convert this mass into grams and express your answer in standard form. (2 marks)

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Why Practise Standard form (scientific notation)?

KNEC Aligned

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