Rounding and accuracy in mathematics enable simplification of numbers while retaining their essence. This section explores rounding techniques to specified degrees of accuracy, focusing on decimal places and significant figures, essential for precision and clarity in mathematical representation.
![Rounding numbers](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2Ffea71f37-96c8-4c72-a271-f0fc64addc63-file.png&w=1080&q=75)
Introduction to Rounding
Rounding transforms numbers into a more manageable form, crucial across various disciplines for simplifying calculations, providing approximations, and enhancing communication.
Importance of Rounding
- Simplification: Facilitates easier calculations.
- Estimation: Offers near-accurate values swiftly.
- Clarity: Improves comprehension and dissemination of numerical data.
Rounding Techniques
Rounding to Decimal Places
Adjusting a number to a fixed number of decimal places.
![Decimal number place value](https://tutorchase-resources-platform-client-production.vercel.app/_next/image?url=https%3A%2F%2Ftutorchase-production.s3.eu-west-2.amazonaws.com%2F7f8018ac-69bf-4fde-839e-164f4f9d6171-file.png&w=1080&q=75)
- Identify the target decimal place.
- Consider the immediate next digit; increment the target if this digit is ≥5.
- Eliminate subsequent digits.
Example: (rounded to 3 decimal places).
Rounding to Significant Figures
Modifying a number to include a specific count of meaningful digits.
- Start at the first non-zero digit.
- Count the desired significant figures.
- Apply rounding based on the subsequent digit; increment the last counted digit if the following digit is ≥5.
Example: (rounded to 3 significant figures).
Worked Examples
Example 1: Rounding to Significant Figures
Question: Round 123.456789 to 4 significant figures.
Solution:
1. Identify and Count: (first 4 significant digits).
2. Next Digit: The 5th digit is 5.
3. Rounding: because the 5th digit ≥5.
Result: when rounded to 4 significant figures.
Example 2: Rounding to Decimal Places
Question: Round £23.987 to 2 decimal places.
Solution:
- Identify Decimal Place: Targeting the 2nd decimal, .
- Next Digit: The 3rd decimal is 7.
- Rounding: since the 3rd digit ≥5.
Result: rounded to 2 decimal places.