EDEXCEL GCSE HIGHER MATHS - What are Limits of Accuracy and Significant Figures

Edexcel GCSE Higher Maths - Limits of Accuracy & Significant Figures

What is a Limit of Accuracy?

The limit of accuracy refers to the smallest possible measurement that can be made with a particular instrument. For example, a ruler with millimeter markings has a limit of accuracy of 1 mm, as it cannot measure anything smaller than that.

Why are Limits of Accuracy Important?

Understanding limits of accuracy is crucial for several reasons:

• Realistic Calculations: When dealing with measurements, it's important to be aware of how precise those measurements are. Using a limit of accuracy greater than the actual precision of the instrument can lead to inaccurate calculations.
• Understanding Uncertainty: Limits of accuracy highlight the inherent uncertainty in measurements. This uncertainty needs to be considered when making conclusions or comparing data.

How to Express Limits of Accuracy:

• Using Inequality Symbols: For example, a measurement of 15 cm accurate to the nearest centimeter can be expressed as 14.5 cm ? length < 15.5 cm.
• Using a Plus or Minus Symbol: For example, a measurement of 15 cm accurate to the nearest centimeter can also be expressed as 15 cm ± 0.5 cm.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. Here are some rules for determining significant figures:

• Non-Zero Digits: All non-zero digits are always significant.
• Zeroes:
  • Between non-zero digits: Zeroes between non-zero digits are significant.
  • Leading zeroes: Zeroes before the first non-zero digit are NOT significant.
  • Trailing zeroes:
    • After a decimal point: Trailing zeroes after a decimal point are significant.
    • Before a decimal point: Trailing zeroes before a decimal point may or may not be significant. Context is needed to determine if they represent accuracy or just place value.

Rounding to Significant Figures:

1. Identify the first significant figure: This is the first non-zero digit from the left.
2. Count the number of significant figures you need: This is determined by the level of accuracy required.
3. Look at the digit to the right of the last significant figure:
   • If it's 5 or greater: Round the last significant figure up.
   • If it's less than 5: Leave the last significant figure as it is.

Limits of Accuracy and Significant Figures in Calculations:

• Addition and Subtraction: The result should be rounded to the same number of decimal places as the measurement with the least number of decimal places.
• Multiplication and Division: The result should be rounded to the same number of significant figures as the measurement with the least number of significant figures.

Examples:

Limit of Accuracy:

• A length measured as 2.5 cm to the nearest 0.1 cm can be expressed as 2.45 cm ? length < 2.55 cm.

Significant Figures:

• 203.05: 5 significant figures
• 0.0045: 2 significant figures
• 1.020 x 10^3: 4 significant figures

Rounding:

• Round 3.14159 to 3 significant figures: 3.14
• Round 0.005678 to 2 significant figures: 0.0057

Remember to always consider the limits of accuracy when working with measurements and ensure that your calculations reflect the appropriate level of precision.