Numbers and Operations
For Singapore O-Level E-Math, Numbers and Operations brings together number sense, prime factorisation, approximation and standard form. Integers include negative and positive whole numbers and zero; rational numbers can be written as a ratio of integers, while real numbers also include values such as √2. Use a number line to compare values: numbers farther right are greater. Keep the sign and type of a number visible, use prime factors to find common factors or multiples, and estimate before trusting a calculator result. This guide focuses on N1 skills beyond index laws; use the dedicated Indices guide for those.
What this guide covers
Number types and ordering, prime factors, HCF and LCM, approximation and estimation, rounding, and standard form. The existing Indices guide covers index laws in depth.
Syllabus reference: 2026 Mathematics 4052, N1, page 5. These are Mentora search groupings, not new official syllabus categories.
Worked example
Write 0.000728 in standard form, then round it to 2 significant figures.
Move the decimal point four places right to get 7.28 × 10⁻⁴. To 2 significant figures this is 7.3 × 10⁻⁴. The coefficient 7.3 is between 1 and 10, and the negative exponent records that the original number is less than 1.
Use prime factors to find an HCF and an LCM
Find the HCF and LCM of 84 and 126 using prime factors.
84 = 2² × 3 × 7 and 126 = 2 × 3² × 7. The HCF uses the smaller powers of shared primes: 2 × 3 × 7 = 42. The LCM uses the larger powers: 2² × 3² × 7 = 252. Check that 42 divides both values and 252 is a multiple of both.
Try three practice checks
Attempt each on paper before revealing the worked answer. These sample particular skills; they do not diagnose the whole topic or establish mastery.
Check 1
Is −3/4 rational, and where does it lie relative to −0.7 on a number line?
Show worked answer
−3/4 = −0.75, which is rational and less than −0.7. Place it to the left of −0.7.
Check 2
Estimate 49.8 × 0.203 before calculating exactly.
Show worked answer
Round to 50 × 0.2 = 10. An exact result near 10 is reasonable; a result near 100 or 1 suggests a place-value error.
Check 3
Round 0.006384 to 2 significant figures and to 3 decimal places.
Show worked answer
To 2 significant figures: 0.0064. To 3 decimal places: 0.006. The first significant digit is the 6, while decimal places count from the decimal point.
Mistakes to watch for
- Leading zeroes locate the decimal point but do not count as significant figures.
- For HCF, take the smallest powers of shared prime factors; for LCM, take the largest powers present.
- In standard form, keep the first factor at least 1 and less than 10, and check the exponent sign against the size of the original number.
If one of these occurs, compare the relevant step with the worked example, then try a different question before drawing conclusions.
Related E-Math guides
Choose a useful next resource
To understand a recurring error rather than relearn the whole skill: Check the 4052 syllabus and revision order.
Published by Mentora · Sources checked 23 Sept 2026
Editorial and source details
Original public examples and answers were checked with automated mathematical/editorial QA. No individual author, human reviewer or independent expert review is recorded.