IGCSE · Practice questions · Ordering quantities and inequality symbols

Convert, compare, convert back.

Six original Cambridge-style questions on ordering numbers and quantities and on using inequality symbols.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

The method

One form, enough decimal places, original answers.

Convert everything to decimals (or to one unit).
Pad to the same number of decimal places, 4 if values are close.
Negatives: further from zero means smaller.
Symbols: the wide end of \(<\) or \(>\) faces the larger number; \(\le\) and \(\ge\) include the end value.
Answer in the original forms, in the order the question asks.

Recall

[3 marks]

Write \(<\), \(>\) or \(=\) in each gap.

(a) \(-6 \ \_\_\ -9\) (b) \(0.3 \ \_\_\ \dfrac{1}{3}\) (c) \(25\% \ \_\_\ \dfrac{1}{4}\)

(a) \(-6 > -9\) ✓
(b) \(\dfrac{1}{3} = 0.333\dots\), so \(0.3 < \dfrac{1}{3}\) ✓
(c) \(25\% = \dfrac{1}{4}\) ✓

Recall

[1 marks]

Write in order, smallest first: \(\ -1.5,\ 0.2,\ -2,\ -0.25,\ 1\).

\(-2,\ -1.5,\ -0.25,\ 0.2,\ 1\) ✓

Calculation

[2 marks]

Write in order, smallest first: \(\ \dfrac{4}{9},\ 0.45,\ 44\%,\ \dfrac{7}{16}\).

\(\dfrac{4}{9} = 0.4444\), \(0.45 = 0.4500\), \(44\% = 0.4400\), \(\dfrac{7}{16} = 0.4375\) ✓
\(\dfrac{7}{16},\ 44\%,\ \dfrac{4}{9},\ 0.45\) ✓

Calculation

[2 marks]

Use your calculator to write in order, smallest first: \(\ \sqrt{17},\ 4.1,\ \dfrac{33}{8},\ \sqrt[3]{70}\).

\(\sqrt{17} = 4.1231\), \(\dfrac{33}{8} = 4.1250\), \(\sqrt[3]{70} = 4.1213\), \(4.1 = 4.1000\) ✓
\(4.1,\ \sqrt[3]{70},\ \sqrt{17},\ \dfrac{33}{8}\) ✓

Analysis

[3 marks]

(a) List the integers \(n\) such that \(-2 \le n < 3\).

(b) The temperature \(t\) °C at a ski resort was above \(-5\) °C and at most 12 °C. Write this as an inequality.

(a) \(-2,\ -1,\ 0,\ 1,\ 2\) ✓
(b) \(-5 < t \le 12\) ✓

Analysis

[3 marks]

Four sprinters' times for a race are: Ana 12.08 s, Ben 12.8 s, Chen \(12\dfrac{3}{25}\) s and Dev 12.085 s.

(a) List the sprinters from fastest to slowest. (b) Find the difference between the fastest and slowest times.

\(12\dfrac{3}{25} = 12.12\). In 3 d.p.: Ana 12.080, Ben 12.800, Chen 12.120, Dev 12.085. ✓
(a) Fastest is the smallest time: Ana, Dev, Chen, Ben ✓
(b) \(12.8 - 12.08 = 0.72\) s ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.