Ordering
Section: Number 1 | Syllabus: Cambridge IGCSE Mathematics (0580)
Ordering
Ordering means arranging quantities by size. The six comparison symbols give a precise way to state how two quantities relate, and the same ideas extend to putting a whole list of numbers - even a mix of fractions, decimals and percentages - in order.
- Comparison symbols:
- = - equal to
- ≠ - not equal to
- > - greater than
- < - less than
- - greater than or equal to
- - less than or equal to
- On a number line, numbers get larger moving to the right - this applies to negative numbers too, so -5 is greater than -8
- To order decimals, compare digit by digit from the left, using the same place value column for each number (pad with trailing zeros if needed)
- To order a mix of fractions, decimals and percentages, convert every value to the same form first, usually decimals
Worked Example: Using Inequality Symbols
- -5 > -8 (-5 is closer to zero, so it is the greater value)
- 0.6 = (3/5) (both are equal to 0.6)
- (7/10) > 0.68 (7/10 = 0.7, and 0.7 is greater than 0.68)
Worked Example: Ordering Decimals
- Question: Write 0.6, 0.56, 0.605 and 0.65 in order, smallest first.
- Step 1: Pad every decimal to the same number of places: 0.600, 0.560, 0.605, 0.650
- Step 2: Compare digit by digit from the left - the tenths digit splits them into 0.56... (tenths digit 5) and the rest (tenths digit 6)
- Step 3: Among 0.600, 0.605 and 0.650, compare the hundredths digit: 0 < 0 < 5, so 0.600 and 0.605 come before 0.650; then compare thousandths to order 0.600 and 0.605
- Answer: 0.56, 0.6, 0.605, 0.65
Worked Example: Ordering a Mix of Fractions, Decimals and Percentages
- Question: Write 68%, 0.7, 3/4 and 7/8 in order, smallest first.
- Step 1: Convert every value to a decimal: 68% = 0.68, 0.7 = 0.7, 3/4 = 0.75, 7/8 = 0.875
- Step 2: Order the decimals: 0.68, 0.7, 0.75, 0.875
- Answer: 68%, 0.7, 3/4, 7/8
Common Mistakes
MistakeThinking -5 is less than -8, by comparing 5 and 8 as if the minus signs were not there
Fixfor negative numbers, the one closer to zero is greater: -5 is further right on the number line than -8, so -5 > -8
MistakeComparing decimals with different numbers of digits as if more digits means a bigger number, e.g. thinking 0.65 < 0.7 because "65" looks bigger than "7"
Fixpad the shorter decimal with trailing zeros first: 0.70 vs 0.65 - now compare digit by digit, and 0.70 is clearly greater
MistakeOrdering a mix of fractions, decimals and percentages by comparing their numbers directly, e.g. treating 3/4 as smaller than 68% because 3 < 68
Fixconvert every value to the same form first (usually decimals) before comparing: 3/4 = 0.75, which is greater than 68% = 0.68
Interactive revision notes, videos and practice questions load below.