GCSE Maths Practice: decimals

Question 8 of 10

This Higher-tier decimals question builds accuracy and confidence when multiplying decimals of different lengths. Understanding place value and estimation is key.

‹ ›

\( \begin{array}{l}\textbf{Calculate } 0.68\times2.25.\end{array} \)

Choose one option:

Estimate before multiplying: 0.7×2≈1.4, so an answer around 1.5 is expected. Use this to check decimal placement.

This Higher-tier decimals problem reinforces precision in multiplying numbers with different decimal lengths. Students must recognise how decimal placement and estimation interact to verify reasonableness.

Concept Focus

When multiplying decimals, the total number of decimal places in the product equals the sum of the decimal places in both factors. Estimation provides a quick mental check that the decimal point is correctly positioned.

Worked Solution

  1. Ignore decimals first: 68 × 225 = 15300.
  2. Count decimal places: 0.68 has 2, 2.25 has 2 → 4 total.
  3. Insert the decimal point: 15300 → 1.5300 = 1.53.

Reasoning & Estimation

Estimate before calculating: 0.68 is roughly two-thirds, and 2.25 ≈ 2. Multiplying gives ≈1.3–1.4. The exact result 1.53 is close, confirming correct placement of the decimal.

Common Errors

  • Forgetting that the total decimal places come from both factors, not just one.
  • Misplacing the decimal point by one position, leading to 0.153 or 15.3.
  • Incorrect estimation—assuming the product of a number less than 1 and a number greater than 2 must exceed 2 (it doesn’t).
  • Rounding too early, instead of finishing exact multiplication first.

Extension Challenge

Apply the same principle to find \(0.684\times2.25\), or \(0.68\times2.254\), rounding to 3 significant figures. This variation introduces more digits while preserving place-value reasoning.

Fraction Connection

0.68 ≈ \(\tfrac{17}{25}\), 2.25 = \(\tfrac{9}{4}\). Multiply fractions: \(\tfrac{17}{25}\times\tfrac{9}{4}=\tfrac{153}{100}=1.53.\) The fractional form confirms the decimal result exactly.

Study Tip

Always align your expectations before calculating. A result near 1.5 makes sense here because multiplying by 2.25 should roughly double 0.68, with a small additional increase. Checking by estimation guards against misplaced decimals and reinforces conceptual understanding of magnitude.

Mastering multi-decimal multiplication is crucial for GCSE success in percentage growth, compound interest, and unit conversion problems where precision and estimation meet.