How do you find the limits of accuracy for a rounded value?

To find the limits of accuracy for a rounded value, identify the range it could have been before rounding.

When a number is rounded to a certain degree of accuracy, such as to the nearest whole number, tenth, or hundredth, it means the original number could have been within a specific range. For example, if a number is rounded to the nearest whole number, say 5, the original number could have been anywhere from 4.5 to 5.5 (but not including 5.5). This range is known as the limits of accuracy.

To determine these limits, you need to consider the smallest and largest values that would round to the given number. If a number is rounded to the nearest whole number, the lower limit is found by subtracting half of the rounding unit from the rounded value, and the upper limit is found by adding half of the rounding unit to the rounded value. For instance, if a number is rounded to the nearest 10, and the rounded value is 50, the lower limit would be 45 (50 - 5) and the upper limit would be 55 (50 + 5).

For rounding to decimal places, the principle is the same. If a number is rounded to one decimal place, such as 3.4, the original number could have been between 3.35 and 3.45. Here, you subtract and add half of the smallest place value (0.05) to the rounded number to find the limits of accuracy.

Understanding these limits helps in analysing the precision of measurements and calculations, ensuring you know the possible range of the original values.