Numeracy

Estimation, Approximation, and Rounding





1. Rounding

Rounding simplifies numbers by expressing them to the nearest unit, ten, hundred, or decimal place.

Key Rules:

  • Round up if the digit is 5 or higher.
  • Round down if the digit is less than 5.

Examples:

  • Nearest 10: 156 160
  • Three Decimal Places: 0.4563948 0.456

Why Round?:

  • Makes calculations easier.
  • Useful for estimating totals in shopping or planning.

2. Estimation

Estimation gives a rough answer, often used to check the reasonableness of detailed calculations.

Steps:

  1. Round numbers to simpler values (nearest 10, 100, etc.).
  2. Perform the calculation.
  3. Adjust up if necessary to ensure you have enough of what’s needed.

Examples:

  • Buying carpet for rooms:
  • Room 1: (3.2 \, {m} * 2.7 \, {m} \approx 3 \, {m} * 3 \, {m} = 9 \, {m}^2)
  • Room 2: (1.16 \, {m} * 2.5 \, {m} \approx 1 \, {m} * 2.5 \, {m} = 2.5 \, {m}^2)
  • Total: (9 + 2.5 = 11.5 \, {m}^2) Round up to 12 ( {m}^2).

3. Practical Uses

  • Shopping: Quickly estimate totals by rounding prices (e.g., \$24.99 \$25).
  • Time: Estimated Time of Arrival (ETA) uses speed and distance for rough arrival times.

4. Special Cases

Tradesperson Estimates:

  • Estimates include time, material costs, and a contingency (~10–20%).
  • Estimates are not binding, but quotes are legally binding if no extra work is added.

5. Benefits of Estimation Skills

  • Cross-check detailed calculations for accuracy.
  • Quickly evaluate budgets, bills, or projects.
  • Confidence in everyday problem-solving without relying solely on a calculator.

Estimation is a practical skill that ensures you’re prepared, whether shopping, planning a project, or checking calculations.


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