Ordering Numbers - The Step-by-Step Method

Worked method: ordering decimals, negatives and fractions together

The digit-count trick breaks down once decimals and negatives are involved.

1. Pad decimals with zerosLine up the decimal points and add zeros so every number has the same number of decimal places. 0.9 becomes 0.90 and 0.85 stays 0.85. Compare digit by digit — 0.90 has the bigger tenths digit (9 vs 8), so 0.9 is larger, even though 0.85 looks like it has more digits. 'More digits = bigger' only works for whole numbers.
2. Order negatives by position, not digit sizeFor negative numbers the bigger the digit, the smaller the value. -7 is smaller than -3 because it sits further left on the number line. Students often assume -7 is bigger because 7 is bigger than 3 — that is the trap. Picture the number line: further left means smaller.
3. Convert everything to decimals firstWhen a set mixes fractions, decimals and negatives, convert every value to a decimal before comparing. 3/4 becomes 0.75, 1/2 becomes 0.5. You cannot compare a fraction to a decimal directly.
4. Build one number lineOnce everything is a decimal, order left to right: most negative first, then closer to zero, then zero, then positives smallest to largest. Negatives always come before positives however large the negative digits look.
5. Check ascending or descending before answeringAscending is smallest to largest; descending is largest to smallest. Re-read the question — a perfectly ordered list written in the wrong direction still loses the marks.
6. Pair-check your final orderBefore finishing, check each neighbouring pair with an inequality sign. If every pair matches the direction the question asked for, the answer is solid.