Ordering numbers

A foundational Edexcel skill that appears on every Paper 1F. Higher students see ordering as part of larger reasoning questions (e.g. "place these in ascending order, then calculate the median").

Ordering integers

On a number line, numbers increase to the right and decrease to the left. Negative numbers: the more negative a number, the smaller it is. So −7 < −3 < 0 < 4 < 11.

Ordering decimals

Compare digit-by-digit from the left (highest place value first). Pad with trailing zeros so all decimals have the same length:

Order: 0.4, 0.42, 0.404, 0.4 → write as 0.400, 0.420, 0.404, 0.400. Compare:

• All start with 0.4.
• Hundredths: 0.420 has 2; 0.404 and 0.400 have 0.
• Thousandths in the 0.40_ pair: 0.404 has 4, 0.400 has 0.
• Ascending: 0.400, 0.404, 0.420 (so 0.4 < 0.404 < 0.42).

Ordering negative decimals

Same digit comparison, but the sign reverses the order: more digits past zero ⇒ more negative ⇒ smaller. −0.6 < −0.45 < −0.4 < −0.04.

Ordering fractions

Three Edexcel-approved strategies:

1. Common denominator (preferred for exact ordering): convert all fractions, then compare numerators.
2. Convert to decimals (calculator allowed on Papers 2 & 3).
3. Cross-compare two at a time using equivalent fractions.

Example: order 2/3, 3/5, 7/10. Common denominator 30: 20/30, 18/30, 21/30. Ascending: 18/30 < 20/30 < 21/30, i.e. 3/5 < 2/3 < 7/10.

Mixed ordering — fractions, decimals, percentages, integers

Convert everything to one form (decimals are easiest) before comparing.

Example: order 3/4, 0.7, 73%. 0.75, 0.7, 0.73 → 0.7 < 0.73 < 0.75 → 0.7 < 73% < 3/4.

Edexcel exam tip

The phrase "in order, smallest first" is ascending; "in order, largest first" is descending. Misreading the direction is one of the most common reasons for losing the easy 2-mark opener.