Ordering integers, decimals and fractions

Ordering numbers is a foundation skill that recurs throughout J560/01 and J560/02 in basic data and number questions. Mistakes here cost easy B1 marks.

Place value and integers

The place value of a digit depends on its column: ones, tens, hundreds, thousands, etc., to the left; tenths, hundredths, thousandths to the right of the decimal point.

To compare positive integers: compare digits left to right. The number with more digits is larger (3142 > 999).

For negative integers: closer to zero is larger (−2 > −7). On a number line, left = smaller, right = larger.

Comparing decimals

Line up the decimal points. Compare digit-by-digit from the left.

Example: order 0.6, 0.06, 0.066, 0.066 from smallest to largest.

• 0.06 (tenths digit 0)
• 0.066 (tenths 0, hundredths 6, thousandths 6)
• 0.6 (tenths 6)

Trick: write each number with the same number of decimal places by adding trailing zeros: 0.600, 0.060, 0.066. Now compare them as if they were integers (600, 60, 66).

Comparing fractions

Three reliable methods:

Method 1 — Common denominator. Convert each fraction to the same denominator; compare numerators.

• Compare 3/8 and 5/12. LCD = 24. → 9/24 and 10/24. So 5/12 > 3/8.

Method 2 — Convert to decimals. Useful with calculator, careful for non-calculator.

• 3/8 = 0.375; 5/12 = 0.4167. So 5/12 > 3/8.

Method 3 — Cross-multiply. Compare a/b and c/d → compare a × d and b × c.

• 3 × 12 = 36; 5 × 8 = 40. Since 40 > 36, 5/12 > 3/8.

Mixed forms

OCR will mix integers, decimals, fractions, and negative numbers in one ordering question. Convert everything to decimals (or all to fractions with a common denominator). Be careful with negatives.

Example: order −1/2, −0.6, 0, 1/3, 0.4 from smallest.

• Decimals: −0.5, −0.6, 0, 0.333, 0.4.
• Sorted: −0.6 < −1/2 < 0 < 1/3 < 0.4.

OCR mark scheme conventions

• Order from smallest = ascending. Order from largest = descending.
• B1 for the correct order, often with M1 for shown working (e.g. converting to common form).