The symbol always points its narrow end towards the smaller value, like an arrow: $3 < 7$.

Convert both sides to the same format — usually decimals — before comparing.

Example: insert $<$, $>$ or $=$ between $\sqrt{0.64}$ and $80\%$.

Evaluate both: $\sqrt{0.64} = 0.8$ and $80\% = 0.8$. They match exactly, so $\sqrt{0.64} = 80\%$.

This is the part that catches people out: for negative numbers, the one with the larger magnitude (the "bigger-looking" number) is actually smaller.

Think of a number line: $-9$ sits further to the left than $-4$, so it represents a smaller value — even though $9 > 4$ as positive numbers.

Exam questions sometimes describe a range in words and ask you to write it using symbols. Translate one phrase at a time, and check whether each end of the range is included:

• "at least $5$" → $x \geqslant 5$ (5 itself is allowed)
• "more than $5$" → $x > 5$ (5 itself is not allowed)
• "at least $5$ but less than $12$" → $5 \leqslant x < 12$

Example: a lift is only safe carrying a load of at least $0$ kg and strictly less than $630$ kg. Write this as an inequality for the load, $L$.

The lower end uses $\leqslant$ because a load of exactly $0$ kg is fine, but the upper end uses $<$ because $630$ kg itself is not safe.

Order the following from smallest to largest: $-\dfrac{1}{2}, \quad 0.4, \quad -0.55, \quad \sqrt{0.16}, \quad 45\%$.

1. Convert each to a decimal: $-\frac{1}{2} = -0.5$, $0.4 = 0.4$, $-0.55 = -0.55$, $\sqrt{0.16} = 0.4$, $45\% = 0.45$.
2. Order the decimals, remembering negatives with a larger magnitude come first:

1. Restate using the original forms:

• Assuming negative numbers order the same way as positives — since $9 > 4$, wrongly concluding $-9 > -4$. It's the reverse: $-9 < -4$.
• Confusing "ascending" and "descending" under time pressure. Ascending = smallest to largest (climbing up); descending = largest to smallest.
• Rounding too early when two converted values are close, which can create a tie that isn't really there.