Summary
The degree of accuracy involves estimating and rounding numbers to simplify calculations while maintaining a similar meaning. It includes rounding to the nearest integer, decimal places, and significant figures, and understanding limits of accuracy for rounded numbers.
- Estimation — a rough calculation of a value, number, or quantity.
Example: Rounding 337 to 340 and 443 to 440 to estimate the total number of marbles as 780. - Rounding to the nearest integer — simplifying a number to the closest whole number.
Example: 152.836 rounds to 153. - Rounding to decimal places — simplifying a number to a specified number of decimal places.
Example: 152.836 rounds to 152.84 when rounded to two decimal places. - Significant figures — the first non-zero digit is the first significant figure.
Example: The first significant figure of 0.00312 is 3. - Limits of accuracy — describe possible values a rounded number could be.
Example: For 105 cm rounded to the nearest cm, the smallest possible value is 104.5 cm, and the largest is 105.5 cm.
Exam Tips
Key Definitions to Remember
- Estimation is a rough calculation of a value.
- Rounding simplifies a number while keeping its meaning similar.
- Significant figures start with the first non-zero digit.
Common Confusions
- Confusing rounding to decimal places with rounding to significant figures.
- Misunderstanding limits of accuracy as exact values.
Typical Exam Questions
- What is the estimated sum of 337 and 443 when rounded to the nearest ten? 780
- What is 152.836 rounded to two decimal places? 152.84
- What are the limits of accuracy for 105 cm rounded to the nearest cm? 104.5 cm and 105.5 cm
What Examiners Usually Test
- Ability to round numbers to different degrees of accuracy.
- Understanding and applying limits of accuracy.
- Estimating sums and products using rounded numbers.
