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Converting to and from standard form
AQA GCSE Mathematics practice questions with step-by-step solutions
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EasyQuestion 1
[2 marks]Write in standard form:
(a) 45,000,000
(b) 0.0000072
Solution for Question 1
MediumQuestion 2
[3 marks]Write as ordinary numbers:
(a) 3.5 × 10⁵
(b) 8.1 × 10⁻⁴
(c) 6.02 × 10⁸
Solution for Question 2
HardQuestion 3
[3 marks]Write in standard form:
(a) 0.4 × 10⁵
(b) 32 × 10⁻³
(c) 560 × 10⁴
Solution for Question 3
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Standard form (scientific notation) writes numbers as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer. It's useful for very large numbers (like 93,000,000 = 9.3 × 10⁷) and very small numbers (like 0.00045 = 4.5 × 10⁻⁴).
To convert TO standard form: move the decimal point until you have a number between 1 and 10. Count how many places you moved - this is the power. Positive power for large numbers, negative for small.
To convert FROM standard form: the power tells you how many places to move the decimal point. Positive power moves right (makes bigger), negative power moves left (makes smaller).
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