Every standard form question from 15 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 1.8. 15 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/12/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Number past paper questions.
0580 Standard Form past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q26
Write these numbers in standard form. (a) 6320 (b) 0.0258
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- Standard form is a number from 1 to 10 times a power of 10.
- 6320 = 6.32 × 1000 = 6.32 × 10³
- Move the decimal point 2 places to the right to get 2.58, so the power is −2.
- 0.0258 = 2.58 × 10⁻²
May/June 2026 · Paper 3 · 0580/31/M/J/26 · Q21
Calculate (8.7 × 10⁸) + (2.4 × 10⁷). Write your answer in standard form.
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- Write both numbers as ordinary numbers: 8.7 × 10⁸ = 870 000 000 and 2.4 × 10⁷ = 24 000 000.
- Add: 870 000 000 + 24 000 000 = 894 000 000.
- Write in standard form: 8.94 × 10⁸
May/June 2026 · Paper 3 · 0580/33/M/J/26 · Q24
(a) Write 0.000 571 in standard form.
(b) Calculate (3.3 × 10⁶) + (12.4 × 10⁵). Give your answer in standard form.
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- Move the decimal point so there is one non-zero digit in front of it: 5.71.
- The point moved 4 places to the right, so the power is −4.
- 5.71 × 10⁻⁴
- Change both to ordinary numbers: 3.3 × 10⁶ = 3 300 000 and 12.4 × 10⁵ = 1 240 000.
- Add: 3 300 000 + 1 240 000 = 4 540 000.
- Write in standard form: 4.54 × 10⁶
Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q26
Write 1.753 × 10⁸ as an ordinary number.
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- × 10⁸ means move the decimal point 8 places to the right.
- 1.753 → 175 300 000 (fill the empty places with zeros).
- 175 300 000
Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q16
Write these numbers in order, starting with the smallest: 9.857 × 10⁻², 3.5 × 10², 1.54 × 10¹, 6.5 × 10⁻²
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- Change each number to an ordinary number so they are easy to compare.
- 9.857 × 10⁻² = 0.09857, 3.5 × 10² = 350, 1.54 × 10¹ = 15.4, 6.5 × 10⁻² = 0.065.
- In order: 0.065, 0.09857, 15.4, 350.
- 6.5 × 10⁻² < 9.857 × 10⁻² < 1.54 × 10¹ < 3.5 × 10²
Oct/Nov 2025 · Paper 1 · 0580/13/O/N/25 · Q27
Sam writes 851 000 in standard form as 85.1 × 10⁴. Explain why 85.1 × 10⁴ is not a number in standard form.
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- In standard form the first number must be at least 1 and less than 10.
- 85.1 is bigger than 10, so it is not in standard form.
- The first number must be at least 1 and less than 10, and 85.1 is bigger than 10.
- The correct form is 8.51 × 10⁵.
Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q23
Calculate 4.6 × 10³⁄1.84 × 10⁵. Give your answer in standard form.
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- Divide the numbers and the powers of 10 separately.
- 4.6 ÷ 1.84 = 2.5.
- 10³ ÷ 10⁵ = 103 − 5 = 10⁻².
- 2.5 × 10⁻²
Oct/Nov 2025 · Paper 3 · 0580/32/O/N/25 · Q21
Calculate (5.6 × 10⁻³) ÷ (2.4 × 10⁻⁵). Write your answer in standard form.
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- Divide the numbers and the powers of 10 separately.
- 5.6 ÷ 2.4 = 2.333…
- 10⁻³ ÷ 10⁻⁵ = 10−3 − (−5) = 10².
- 2.33 × 10²
- Check: 2.333… is between 1 and 10, so this is in standard form ✓
May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q25
(a) Write 32 500 in standard form.
(b) Write 5.6 × 10−3 as an ordinary number.
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- Standard form is a number between 1 and 10 times a power of 10.
- 32 500 = 3.25 × 10 000, and 10 000 = 10⁴.
- 32 500 = 3.25 × 104
- 10−3 means divide by 1000, so move the decimal point 3 places to the left.
- 5.6 → 0.56 → 0.056 → 0.0056
0580 Standard Form past paper questions: Extended (Papers 2 and 4)
May/June 2026 · Paper 2 · 0580/21/M/J/26 · Q19
710 000.03 = (7.1 × 10ᵃ) + (3 × 10ᵇ). Find the value of a and the value of b.
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- Split the number into its two parts: 710 000.03 = 710 000 + 0.03.
- 710 000 = 7.1 × 100 000 = 7.1 × 10⁵.
- 0.03 = 3 × 0.01 = 3 × 10⁻².
- a = 5, b = −2
May/June 2026 · Paper 2 · 0580/23/M/J/26 · Q9
(a) Write 7.83 × 10⁻² as an ordinary number.
(b) Work out (5.5 × 10⁶) × (2 × 10⁻³). Give your answer in standard form.
Show solution
- 10⁻² means divide by 100, so move the decimal point 2 places to the left.
- 7.83 → 0.783 → 0.0783
- Multiply the numbers and the powers of 10 separately.
- 5.5 × 2 = 11. 10⁶ × 10⁻³ = 106 + (−3) = 10³.
- 11 × 10³ is not standard form because 11 is bigger than 10. 11 = 1.1 × 10.
- 11 × 10³ = 1.1 × 10⁴, so the answer is 1.1 × 10⁴
Feb/Mar 2026 · Paper 2 · 0580/22/F/M/26 · Q12
(a) Write 230 000 in standard form.
(b) Work out (4.2 × 10³²) − (4.2 × 10³¹). Give your answer in standard form.
(c) Work out (8 × 10⁵¹)1/3. Give your answer in standard form.
Show solution
- Standard form is a number from 1 to 10 times a power of 10.
- 230 000 = 2.3 × 100 000 = 2.3 × 10⁵
- Write both with the same power: 4.2 × 10³¹ = 0.42 × 10³².
- Subtract: (4.2 − 0.42) × 10³² = 3.78 × 10³²
- A power of 1⁄3 means cube root. Find the cube root of each part.
- ∛8 = 2, and (10⁵¹)1/3 = 1051 ÷ 3 = 10¹⁷.
- 2 × 10¹⁷
Oct/Nov 2025 · Paper 2 · 0580/21/O/N/25 · Q15
(a) Write 66 000 in standard form. (b) Work out (3.7 × 10⁸) + (3.7 × 10⁷). Give your answer in standard form.
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- Standard form is a number from 1 to 10 times a power of 10.
- 66 000 = 6.6 × 10 000 = 6.6 × 10⁴
- Write both numbers with the same power of 10: 3.7 × 10⁷ = 0.37 × 10⁸.
- Add: 3.7 × 10⁸ + 0.37 × 10⁸ = (3.7 + 0.37) × 10⁸.
- 4.07 × 10⁸
Oct/Nov 2025 · Paper 4 · 0580/43/O/N/25 · Q11
Use a number from the box to complete each statement: 2.89 × 10⁻¹, 1.3 × 10¹², 8.3 × 10¹, 9 × 10¹¹, 2.03 × 10⁻⁵, 0.3 × 10⁻².
The number that is not written in standard form is … . The largest number is … . The smallest number is … .
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- A number in standard form is A × 10ⁿ with 1 ≤ A < 10.
- 0.3 is less than 1, so the one not in standard form is 0.3 × 10⁻²
- For numbers in standard form, the biggest power of 10 is the largest number. 10¹² is the biggest power.
- Largest = 1.3 × 10¹²
- The most negative power of 10 gives the smallest number. 10⁻⁵ is the most negative.
- Smallest = 2.03 × 10⁻⁵
- Tip: 0.3 × 10⁻² = 3 × 10⁻³, which is bigger than 2.03 × 10⁻⁵.
May/June 2025 · Paper 2 · 0580/22/M/J/25 · Q11
(a) Write 0.007 08 in standard form.
(b) Work out (3.8 × 1022) + (3.8 × 1023). Give your answer in standard form.
Show solution
- Move the decimal point to the right until the number is between 1 and 10: 0.007 08 → 7.08. That is 3 places.
- Moving to the right means a negative power.
- 7.08 × 10−3
- Write both numbers with the same power of 10: 3.8 × 1023 = 38 × 1022.
- Add: 3.8 × 1022 + 38 × 1022 = 41.8 × 1022.
- 41.8 is not between 1 and 10, so adjust: 41.8 × 1022 = 4.18 × 1023.
- 4.18 × 1023
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