GCSE Maths Practice: powers-and-roots

Question 7 of 10

This question tests your understanding of cubing decimals — a useful skill in GCSE Powers and Roots and real-world volume calculations.

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\( \begin{array}{l} \text{What is } 0.5^3? \end{array} \)

Choose one option:

When cubing decimals smaller than one, the result becomes smaller. Use estimation to check that your answer makes sense.

Understanding Cubes of Decimals

Cubing a decimal means multiplying it by itself three times. The process follows exactly the same rules as cubing whole numbers. However, since decimals are smaller than one, each multiplication makes the result smaller. This idea is important when dealing with volume, density, and scaling problems in GCSE Maths.

Concept Overview

The cube of a number tells us how many unit cubes would fill a cube with sides of that length. If the side length is less than one, the volume is less than one cubic unit. This is why cubing decimals leads to smaller results.

Step-by-Step Method

  1. Write the decimal clearly inside brackets before applying the power.
  2. Multiply the number by itself twice more.
  3. Check the result by counting decimal places or using a calculator for precision.

Worked Examples (Different Numbers)

  • \(0.2^3 = 0.008\)
  • \(0.3^3 = 0.027\)
  • \(0.4^3 = 0.064\)

In every case, the cube of a decimal less than one becomes smaller. This pattern helps in estimating answers during exams.

Common Mistakes

  • Confusing cubing with multiplying by three — they are not the same operation.
  • Forgetting to multiply three times.
  • Misplacing the decimal point when squaring or cubing decimals.

Real-Life Applications

Cubing decimals is used in physics and everyday measurements. For example, when calculating the volume of a cube-shaped container with edges less than one metre, the result is a small decimal value. Similarly, scientists use cubes of decimals when converting units like centimetres to litres or in density calculations.

Quick FAQ

  • Q1: Why does cubing a decimal make it smaller?
    A1: Because multiplying by a number less than one repeatedly reduces the overall product.
  • Q2: Does this rule apply to all decimals?
    A2: Yes, any decimal between 0 and 1 gets smaller when raised to a positive power.
  • Q3: What happens when you cube a number greater than one?
    A3: The result becomes larger, as each multiplication increases the size.

Study Tip

Practise cubing small decimals such as 0.2, 0.3, and 0.5. Notice the pattern: the answers quickly become very small. Understanding this helps with estimation and checking the reasonableness of answers in GCSE questions involving powers, ratios, and scaling.