IGCSE · Mathematics 0580 · Number

Standard form: IGCSE Mathematics questions with answers

Free Standard form questions for IGCSE Mathematics (0580), part of Number. Each question has the answer and the marking points an examiner would look for.

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Standard form practice questions

Question 1Structured · 11 marksA* challenge

Do not use a calculator in this question.

(a)

Find the number of digits in 1625 × 12530 when it is written out in full.

[3]
(b)

p and q are positive integers with p + q = 30.
When 2p × 5q is written out in full, it has exactly 15 digits and its first digit is 1.
Find p and q. Show that there are no other possibilities.

[5]
(c)

p and q are positive integers with p + q = 30. Find, in standard form, the largest value of 2p × 5q that has fewer than 15 digits.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)94
2100 × 590 M1
= 210 × 1090 = 1024 × 1090 M1
94 A1
3
(b)p = 17, q = 13
2p × 5q = 1015 × (25)p − 15 M1
15 digits: 1014 ≤ number < 1015, so 0.1 ≤ (25)p − 15 < 1 M1
p − 15 = 1 or 2 only (0.4, 0.16; 0.064 < 0.1) A1
p = 16 gives 4 × 1014, first digit 4 M1
p = 17 gives 1.6 × 1014: p = 17, q = 13 A1
5
(c)6.4 × 1013
2p × 5q decreases as p increases, so the least p with fewer than 15 digits is needed: p = 18 M1
218 × 512 = 26 × 1012 M1
6.4 × 1013 A1
3
Question 2Structured · 2 marks

Calculate (1.8 × 106) ÷ (2 × 103).
Give your answer in standard form.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
9 × 102
9 and 102 seen M1
9 × 102 A1
2
Question 3Structured · 2 marks

Calculate (3.6 × 105) ÷ (4 × 104).
Give your answer in standard form.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
9 × 100
9 and 100 seen M1
9 × 100 A1
2
Question 4Structured · 2 marks

Calculate (4 × 108) ÷ (5 × 10−4).
Give your answer in standard form.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
8 × 1011
8 and 1011 seen M1
8 × 1011 A1
2
Question 5Structured · 2 marks

Calculate (3.6 × 107) ÷ (9 × 10−1).
Give your answer in standard form.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
4 × 107
4 and 107 seen M1
4 × 107 A1
2

More Number questions

Types of numberSetsPowers & rootsFractions, decimals & percentagesThe four operationsIndices IEstimationLimits of accuracyRatio & proportionRatesPercentagesTimeMoneyExponential growth & decaySurds

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Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in