Standard form
Number
- Crossover
- Non-calculator
- 8 questions
- 29 marks
Questions marked Higher are aimed at the Higher tier.
These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.
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Write $45000$ in standard form.
2 marks
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Write $0.0062$ in standard form.
2 marks
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Write $3.04 \times 10^{5}$ and $7.1 \times 10^{-4}$ as ordinary numbers.
3 marks
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Work out $(3 \times 10^{4}) \times (4 \times 10^{3})$. Give the answer in standard form.
3 marks
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Work out $(8.4 \times 10^{6}) \div (2 \times 10^{4})$. Give the answer in standard form.
4 marks
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Work out $(3.6 \times 10^{3}) + (2.4 \times 10^{4})$. Give the answer in standard form.
4 marks
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Town A has $6.4 \times 10^{5}$ people and town B has $2.5 \times 10^{6}$ people. How many more people live in B than in A? How many times as big as A is B, to $2$ significant figures? Higher
5 marks
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A grain of sand has mass $4 \times 10^{-5}$ g. Find the mass, in grams, of $8 \times 10^{6}$ grains. A bucket holds $2.4$ kg of these grains. How many grains is that? Higher
6 marks
Mark scheme
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Answer. $4.5 \times 10^{4}$
- Move the decimal point $4$ places.
- $4.5 \times 10^{4}$
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Answer. $6.2 \times 10^{-3}$
- The first significant digit is $3$ places after the decimal point.
- $6.2 \times 10^{-3}$
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Answer. $304000$ and $0.00071$
- $3.04 \times 10^{5} = 304000$.
- $7.1 \times 10^{-4} = 0.00071$.
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Answer. $1.2 \times 10^{8}$
- $12 \times 10^{7}$
- $1.2 \times 10^{8}$
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Answer. $4.2 \times 10^{2}$
- $8.4 \div 2 = 4.2$
- $10^{6} \div 10^{4} = 10^{2}$
- $4.2 \times 10^{2}$
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Answer. $2.76 \times 10^{4}$
- $3600 + 24000 = 27600$
- $2.76 \times 10^{4}$
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Answer. $1.86 \times 10^{6}$ more people, and $3.9$ times as big
- $2.5 \times 10^{6} - 6.4 \times 10^{5} = 1.86 \times 10^{6}$.
- $\dfrac{2.5 \times 10^{6}}{6.4 \times 10^{5}} = 3.90625$.
- To $2$ s.f. this is $3.9$.
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Answer. $3.2 \times 10^{2}$ g, and $6 \times 10^{7}$ grains
- $4 \times 10^{-5} \times 8 \times 10^{6} = 32 \times 10^{1} = 3.2 \times 10^{2}$ g.
- $2.4$ kg $= 2.4 \times 10^{3}$ g.
- $\dfrac{2.4 \times 10^{3}}{4 \times 10^{-5}} = 6 \times 10^{7}$.