What this guide covers
Sec 1 number ordering and estimation. Standard form and index laws belong in later or separately taught work and are not assessed here.
Compare using one representation
Convert fractions to decimals, or put both values on the same number line. With negative values, the number farther left is smaller.
- Although 0.8 is greater than 0.75, −0.8 is smaller than −0.75.
- A terminating decimal can be written as a fraction of integers; that gives another way to compare it exactly.
Order three close negative values
Place −0.65, −23 and −0.7 in ascending order.
- Write −23 as approximately −0.6667.
- On a number line, −0.7 is left of −0.6667, which is left of −0.65.
- Ascending order is −0.7, −23, −0.65.
Check: Since 0.7 > 23 > 0.65, reversing the signs reverses their order.
Use an estimate to check multiplication
Estimate 19.8 × 0.49, then calculate it exactly.
- Use nearby values: 20 × 0.5 = 10.
- Exactly, 19.8 × 0.49 = 9.702.
- The exact result is close to 10, so its place value is plausible.
Check: An answer near 100 would be inconsistent with multiplying by a number below 1.
Estimate before trusting a result
Round each factor to a nearby convenient value, calculate the estimate, then compare its size with the exact answer.
- An estimate is a check, not a replacement for an exact answer when one is required.
- Leading zeroes locate a decimal point; they are not significant digits.
Try it yourself
Work on paper, then compare the steps. These checks do not establish mastery.
Which is smaller: −0.42 or −25? Explain.
−25=−0.4. Since −0.42 lies farther left than −0.4, −0.42 is smaller.
Estimate 31.2 ÷ 0.78 using convenient numbers.
About 32 ÷ 0.8 = 40. An exact result should be near 40, not near 4 or 400.
Round 0.04786 to 2 significant figures.
0.048. The first significant digit is 4; the next digit is 7 and the following 8 rounds 7 up to 8.
Where this connects
- See all Sec 1 topic areas →
Put number ordering beside ratio, percentage and rate work at this level.
- Later: prime-factor challenge →
The Upper Secondary guide keeps these foundations as a refresher and adds harder number reasoning.
Sources and scope
Original Mentora examples and questions. Sec 1 N1 level placement follows the MOE G2/G3 Mathematics syllabus and the existing Sec 1 assessment audit; no school-paper wording is reproduced.