AQA · Mathematics · 8300
GCSE Maths: Standard form: multiplication
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Standard form: multiplication (Corbettmaths Video 302), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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Write 35000 in standard form.
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3.5 × 10⁴
Write 1.2 × 10³ as an ordinary number.
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1200
Write 0.000345 in standard form.
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3.45 × 10⁻⁴
Why is 481 × 10⁵ not valid standard form for 48100000?
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In standard form, the number before the multiplication sign must be between 1 and 10. 481 is not in this range; the correct answer is 4.81 × 10⁷.
Why is 5.4 × 10³ incorrect standard form for 0.0054?
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For numbers less than 1, the exponent should be negative. The correct answer is 5.4 × 10⁻³.
Write 375 × 10⁶ in standard form.
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3.75 × 10⁸. (Move the decimal point in 375 to get a coefficient between 1 and 10, adjusting the exponent accordingly: 375 = 3.75 × 10², so 375 × 10⁶ = 3.75 × 10⁸)
Calculate (4 × 10⁵) × (2 × 10⁴) and give the answer in standard form.
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8 × 10⁹. (Multiply the coefficients: 4 × 2 = 8; add the exponents: 5 + 4 = 9)
Calculate (3 × 10⁴) ÷ (6 × 10⁻³) and give the answer in standard form.
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5 × 10⁶. (Divide the coefficients: 3 ÷ 6 = 0.5; subtract the exponents: 4 − (−3) = 7; then 0.5 × 10⁷ = 5 × 10⁶)
Calculate (5 × 10⁴)² and give the answer in standard form.
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2.5 × 10⁹. (Square the coefficient: 5² = 25; multiply the exponent by 2: 4 × 2 = 8; then 25 × 10⁸ = 2.5 × 10⁹)
How do you add numbers in standard form with different exponents, such as (2.6 × 10⁶) + (7.1 × 10⁵)?
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Convert to ordinary numbers or adjust exponents to match, then add. Example: 2.6 × 10⁶ = 26 × 10⁵, so (26 × 10⁵) + (7.1 × 10⁵) = 33.1 × 10⁵ = 3.31 × 10⁶.
Write 2500 kg in grams, giving your answer in standard form.
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2.5 × 10⁶ g. (2500 kg × 1000 g/kg = 2500000 g = 2.5 × 10⁶ g)
Calculate ∛(8 × 10¹²) and give the answer in standard form.
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2 × 10⁴. (∛8 = 2; ∛10¹² = 10⁴)
When converting a number from standard form to ordinary form, a ? exponent means the number is less than 1.
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negative
What is the relationship between circumference and diameter of a circle?
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Circumference = π × diameter (or diameter = circumference ÷ π)
When solving a speed-distance-time problem, what unit conversion is needed if distance is in km and speed is in m/s?
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Convert km to m by multiplying by 1000 (or convert m to km by dividing by 1000).
What is the formula for surface area of a sphere?
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A = 4πr², where r is the radius.
When dividing numbers in standard form, how do you combine the powers of 10?
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Subtract the exponents (e.g., 10^a ÷ 10^b = 10^(a-b)).
In standard form a × 10^n, the value of a must satisfy ?.
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1 ≤ a < 10
When calculating a percentage, what is the formula?
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(part ÷ whole) × 100
The radius of a sphere is ? its diameter.
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half
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