Ordering.
Compare the values, choose a common form and put every quantity in its place.
Order by magnitude · use =, ≠, >, <, ≥ and ≤ · compare mixed forms and units
Magnitude is position on a number line
Ordering is deciding which quantity is smaller and which is larger. Picture a number line: moving right increases the value. This also explains negatives, where −2 lies to the right of −5 even though its digit is smaller.
The inequality symbols record that position. Read 3 < 7 as “3 is less than 7”. The open end faces the larger value. Adding a line underneath includes equality, so x ≤ 7 allows x to be 7 as well as smaller values.
To order quantities, compare their values. Ascending means smallest to largest; descending means largest to smallest.
Equal / not equal
0.5 = 12, but 0.5 ≠ 13.
Greater than / less than
5 > 2 and −4 < −1. The open end faces the greater value.
Including equality
x ≥ 3 means x is greater than or equal to 3. x ≤ 3 means at most 3.
Pause and explainWhich is larger, −1 or −6, and why?
−1 is larger because it lies further right on the number line, closer to zero.
Choose a common form
Comparisons become awkward when one value is a fraction, another a percentage and another a decimal. First put them into one shared language, just as you would convert metres and centimetres before comparing lengths.
Choose the common form that makes the calculation simplest. Decimals often work well for mixed representations, while a common denominator works well for fractions. Preserve enough digits to tell the values apart; rounding first can make different numbers appear equal.
Put 0.62, 58, 61% and 0.602 in ascending order.
Convert to decimals and align the places:
Compare tenths, then hundredths, then thousandths.
Fractions
Use a common denominator: 56 = 2024 and 78 = 2124, so 56 < 78.
Measurements
Convert to the same unit: 0.8 m = 80 cm. Therefore 75 cm < 0.8 m < 820 mm because 820 mm = 82 cm.
Pause and explainWhy compare 0.6 as 0.600 with 0.597?
The extra zeros do not change its value, but aligning place values makes the first different digit easy to identify.
Your turn. Compare like with like.
For each comparison, first decide whether you need a common numerical form, a common unit, or a number-line sketch. Do that preparation before choosing an inequality symbol.
When a list is required, check whether the question asks for ascending or descending order. Re-read your final answer from left to right and confirm that every neighbouring pair follows the requested direction.
Insert <, > or =: −0.7 … −0.65; 35 … 60%; 0.08 … 0.8.
Reveal worked answer
Order −1.2, −54, −1.02 and −120% from smallest to largest.
Reveal worked answer
Write “the temperature T is at least −3°C but below 5°C” using inequalities.