IGCSE Maths 0580 Standard Form Past Paper Questions and Worked Solutions

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IGCSE Maths (0580) · Number · 1.8

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)

12 marksCore

May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q26

Write these numbers in standard form. (a) 6320 (b) 0.0258

Show solution
Part (a)
  1. Standard form is a number from 1 to 10 times a power of 10.
  2. 6320 = 6.32 × 1000 = 6.32 × 10³
Answer 6.32 × 10³
Part (b)
  1. Move the decimal point 2 places to the right to get 2.58, so the power is −2.
  2. 0.0258 = 2.58 × 10⁻²
Answer 2.58 × 10⁻²
22 marksCore

May/June 2026 · Paper 3 · 0580/31/M/J/26 · Q21

Calculate (8.7 × 10⁸) + (2.4 × 10⁷). Write your answer in standard form.

Show solution
  1. Write both numbers as ordinary numbers: 8.7 × 10⁸ = 870 000 000 and 2.4 × 10⁷ = 24 000 000.
  2. Add: 870 000 000 + 24 000 000 = 894 000 000.
  3. Write in standard form: 8.94 × 10⁸
Answer 8.94 × 10⁸
33 marksCore

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.

Show solution
Part (a)
  1. Move the decimal point so there is one non-zero digit in front of it: 5.71.
  2. The point moved 4 places to the right, so the power is −4.
  3. 5.71 × 10⁻⁴
Answer 5.71 × 10⁻⁴
Part (b)
  1. Change both to ordinary numbers: 3.3 × 10⁶ = 3 300 000 and 12.4 × 10⁵ = 1 240 000.
  2. Add: 3 300 000 + 1 240 000 = 4 540 000.
  3. Write in standard form: 4.54 × 10⁶
Answer 4.54 × 10⁶
41 markCore

Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q26

Write 1.753 × 10⁸ as an ordinary number.

Show solution
  1. × 10⁸ means move the decimal point 8 places to the right.
  2. 1.753 → 175 300 000 (fill the empty places with zeros).
  3. 175 300 000
Answer 175 300 000
52 marksCore

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

Show solution
  1. Change each number to an ordinary number so they are easy to compare.
  2. 9.857 × 10⁻² = 0.09857, 3.5 × 10² = 350, 1.54 × 10¹ = 15.4, 6.5 × 10⁻² = 0.065.
  3. In order: 0.065, 0.09857, 15.4, 350.
  4. 6.5 × 10⁻² < 9.857 × 10⁻² < 1.54 × 10¹ < 3.5 × 10²
Answer 6.5 × 10⁻² < 9.857 × 10⁻² < 1.54 × 10¹ < 3.5 × 10²
61 markCore

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.

Show solution
  1. In standard form the first number must be at least 1 and less than 10.
  2. 85.1 is bigger than 10, so it is not in standard form.
  3. The first number must be at least 1 and less than 10, and 85.1 is bigger than 10.
  4. The correct form is 8.51 × 10⁵.
Answer The first number must be at least 1 and less than 10, and 85.1 is bigger than 10.
72 marksCore

Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q23

Calculate 4.6 × 10³⁄1.84 × 10⁵. Give your answer in standard form.

Show solution
  1. Divide the numbers and the powers of 10 separately.
  2. 4.6 ÷ 1.84 = 2.5.
  3. 10³ ÷ 10⁵ = 103 − 5 = 10⁻².
  4. 2.5 × 10⁻²
Answer 2.5 × 10⁻²
82 marksCore

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.

Show solution
  1. Divide the numbers and the powers of 10 separately.
  2. 5.6 ÷ 2.4 = 2.333…
  3. 10⁻³ ÷ 10⁻⁵ = 10−3 − (−5) = 10².
  4. 2.33 × 10²
  5. Check: 2.333… is between 1 and 10, so this is in standard form ✓
Answer 2.33 × 10²
92 marksCore

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.

Show solution
Part (a)
  1. Standard form is a number between 1 and 10 times a power of 10.
  2. 32 500 = 3.25 × 10 000, and 10 000 = 10⁴.
  3. 32 500 = 3.25 × 104
Answer 3.25 × 104
Part (b)
  1. 10−3 means divide by 1000, so move the decimal point 3 places to the left.
  2. 5.6 → 0.56 → 0.056 → 0.0056
Answer 0.0056

0580 Standard Form past paper questions: Extended (Papers 2 and 4)

102 marksExtended

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.

Show solution
  1. Split the number into its two parts: 710 000.03 = 710 000 + 0.03.
  2. 710 000 = 7.1 × 100 000 = 7.1 × 10⁵.
  3. 0.03 = 3 × 0.01 = 3 × 10⁻².
  4. a = 5, b = −2
Answer a = 5, b = −2
113 marksExtended

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
Part (a)
  1. 10⁻² means divide by 100, so move the decimal point 2 places to the left.
  2. 7.83 → 0.783 → 0.0783
Answer 0.0783
Part (b)
  1. Multiply the numbers and the powers of 10 separately.
  2. 5.5 × 2 = 11. 10⁶ × 10⁻³ = 106 + (−3) = 10³.
  3. 11 × 10³ is not standard form because 11 is bigger than 10. 11 = 1.1 × 10.
  4. 11 × 10³ = 1.1 × 10⁴, so the answer is 1.1 × 10⁴
Answer 1.1 × 10⁴
125 marksExtended

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
Part (a)
  1. Standard form is a number from 1 to 10 times a power of 10.
  2. 230 000 = 2.3 × 100 000 = 2.3 × 10⁵
Answer 2.3 × 10⁵
Part (b)
  1. Write both with the same power: 4.2 × 10³¹ = 0.42 × 10³².
  2. Subtract: (4.2 − 0.42) × 10³² = 3.78 × 10³²
Answer 3.78 × 10³²
Part (c)
  1. A power of 1⁄3 means cube root. Find the cube root of each part.
  2. ∛8 = 2, and (10⁵¹)1/3 = 1051 ÷ 3 = 10¹⁷.
  3. 2 × 10¹⁷
Answer 2 × 10¹⁷
133 marksExtended

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.

Show solution
Part (a)
  1. Standard form is a number from 1 to 10 times a power of 10.
  2. 66 000 = 6.6 × 10 000 = 6.6 × 10⁴
Answer 6.6 × 10⁴
Part (b)
  1. Write both numbers with the same power of 10: 3.7 × 10⁷ = 0.37 × 10⁸.
  2. Add: 3.7 × 10⁸ + 0.37 × 10⁸ = (3.7 + 0.37) × 10⁸.
  3. 4.07 × 10⁸
Answer 4.07 × 10⁸
142 marksExtended

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 … .

Show solution
  1. A number in standard form is A × 10ⁿ with 1 ≤ A < 10.
  2. 0.3 is less than 1, so the one not in standard form is 0.3 × 10⁻²
  3. For numbers in standard form, the biggest power of 10 is the largest number. 10¹² is the biggest power.
  4. Largest = 1.3 × 10¹²
  5. The most negative power of 10 gives the smallest number. 10⁻⁵ is the most negative.
  6. Smallest = 2.03 × 10⁻⁵
  7. Tip: 0.3 × 10⁻² = 3 × 10⁻³, which is bigger than 2.03 × 10⁻⁵.
Answer 0.3 × 10⁻² 1.3 × 10¹² 2.03 × 10⁻⁵
153 marksExtended

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
Part (a)
  1. Move the decimal point to the right until the number is between 1 and 10: 0.007 08 → 7.08. That is 3 places.
  2. Moving to the right means a negative power.
  3. 7.08 × 10−3
Answer 7.08 × 10−3
Part (b)
  1. Write both numbers with the same power of 10: 3.8 × 1023 = 38 × 1022.
  2. Add: 3.8 × 1022 + 38 × 1022 = 41.8 × 1022.
  3. 41.8 is not between 1 and 10, so adjust: 41.8 × 1022 = 4.18 × 1023.
  4. 4.18 × 1023
Answer 4.18 × 1023

Question papers used on this page

All standard form questions above, listed by 0580 question paper code.

QP codeFile namePaperQuestions
0580/12/M/J/260580_s26_qp_12May/June 2026 · Paper 1 (Core)Q26
0580/21/M/J/260580_s26_qp_21May/June 2026 · Paper 2 (Extended)Q19
0580/23/M/J/260580_s26_qp_23May/June 2026 · Paper 2 (Extended)Q9
0580/31/M/J/260580_s26_qp_31May/June 2026 · Paper 3 (Core)Q21
0580/33/M/J/260580_s26_qp_33May/June 2026 · Paper 3 (Core)Q24
0580/22/F/M/260580_m26_qp_22Feb/Mar 2026 · Paper 2 (Extended)Q12
0580/11/O/N/250580_w25_qp_11Oct/Nov 2025 · Paper 1 (Core)Q26
0580/12/O/N/250580_w25_qp_12Oct/Nov 2025 · Paper 1 (Core)Q16
0580/13/O/N/250580_w25_qp_13Oct/Nov 2025 · Paper 1 (Core)Q27
0580/21/O/N/250580_w25_qp_21Oct/Nov 2025 · Paper 2 (Extended)Q15
0580/31/O/N/250580_w25_qp_31Oct/Nov 2025 · Paper 3 (Core)Q23
0580/32/O/N/250580_w25_qp_32Oct/Nov 2025 · Paper 3 (Core)Q21
0580/43/O/N/250580_w25_qp_43Oct/Nov 2025 · Paper 4 (Extended)Q11
0580/11/M/J/250580_s25_qp_11May/June 2025 · Paper 1 (Core)Q25
0580/22/M/J/250580_s25_qp_22May/June 2025 · Paper 2 (Extended)Q11

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