Edexcel GCSE Maths: Rounding and Estimation

Edexcel GCSE Maths: Rounding and Estimation

1. Rounding to Significant Figures

Significant figures (s.f.) indicate the number of digits that contribute to the precision of a number. Here's how to round to s.f.:

• Identify the first non-zero digit. This is the first significant figure.
• Count the required number of significant figures.
• 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.
• Replace all digits after the last significant figure with zeros if the number is an integer. If it's a decimal, just remove the digits.

Example: Round 3.14159 to 3 s.f.

1. First non-zero digit: 3
2. Count 3 s.f.: 3.14
3. Digit to the right: 1 (less than 5)
4. Result: 3.14

2. Rounding to Decimal Places

Decimal places (d.p.) specify the number of digits after the decimal point.

• Count the required number of decimal places.
• Look at the digit in the next decimal place.
  • If it's 5 or greater, round the last decimal place up.
  • If it's less than 5, leave the last decimal place as it is.
• Remove all digits after the last decimal place.

Example: Round 2.71828 to 2 d.p.

1. Count 2 d.p.: 2.71
2. Digit to the right: 8 (greater than 5)
3. Result: 2.72

3. Approximating Calculations

Approximating calculations involves using rounded numbers to estimate the result. This is useful for quickly getting a sense of the answer.

• Round all numbers to a convenient level of accuracy (e.g., nearest whole number, 1 s.f.).
• Perform the calculation using the rounded numbers.

Example: Approximate 12.3 x 4.8

• Round 12.3 to 12 and 4.8 to 5.
• Approximate calculation: 12 x 5 = 60

4. Error Bounds

Error bounds represent the range within which the true value of a rounded number lies.

• Upper bound: The largest possible value of the rounded number.
• Lower bound: The smallest possible value of the rounded number.

Example: The error bounds for 12.3 rounded to 1 s.f. are:

• Upper bound: 12.5
• Lower bound: 11.5

5. Using Approximations in Complex Calculations

Approximations can simplify complex calculations, making them easier to perform mentally.

• Identify the most significant numbers or parts of the calculation.
• Round these numbers to convenient values.
• Perform the calculation with the rounded values.

Example: Approximate (4.87 + 12.1)/3.92

• Round 4.87 to 5, 12.1 to 12, and 3.92 to 4.
• Approximate calculation: (5 + 12)/4 = 4.25

Remember: Rounding and estimation techniques provide powerful tools for simplifying calculations and understanding the magnitude of numbers in real-world applications. They are valuable skills for gaining insight into the accuracy and potential errors involved in calculations.