If a number is rounded to the nearest ten and the number is 30, what are the highest and lowest numbers that the original number could have been to end up with the resulting 30? So in this case, the answer would have been 25 and 34.999...infinite number of 9s...999

By international agreement, we give the higher number as 35. So we are rounding it slightly up. Now, the 25 is the lowest number that would round to 30 and the 35 is just above the highest number that would round down to 30. We call the 25 - the lower bound and the 35 - the upper bound.

The actual number could have been anything between 25 and 35. Those two numbers are the limits of what would round to 30.

Bounds and Accuracy

This sheet has various examples of problems involving the use of bounds and accuracy.

Shapes and Bounds

Dimensions on different shapes have been given to a particular degree of accuracy. Calculate the limits of the volume and surface area of each shape.

Bounds and Error Intervals

This is a good place to start the work on bounds as it begins with looking at the limits of intervals. It then moves onto suitable degrees of accuracy.

Shapes and Bounds Video

This video discusses how to calculate the shapes and bounds work and examines how we choose a suitable degree of accuracy.

Rounding, Bounds and Limits

This video starts with rounding, then moves onto the error intervals that would exist following rounding and finally moves onto how to apply this information to problems such as area.

Bounds and Error Intervals of Shapes

Examine the area of shapes using bounds to undo any rounding that has been performed.

Bounds and Error Intervals of Shapes Templates

Template to help students do the sheet on bounds and error intervals with shape.

Answers to Bounds Sheet

Answers to the Bounds sheet.

Combining Operations for Bounds

When combining operations for bounds, you have to be careful with your selection of upper or lower bounds to ensure you achieve the maximum or minimum desired.

Presentation Introducing Bounds and Error Intervals

Presentation designed to give a brief overview of Bounds and Error Intervals.

Combining Operations for Bounds Multiplication and Addition

This video works through an example from the shapes sheet provided above. Looks at combining operations with bounds with multiplication.

Combining Operations for Bounds Division

This video works through an example for finding the bounds for density for a ball. Looks at combining operations with bounds with division.

Bounds Assessment Feedback Sheet

Feedback on Bounds and Error Intervals Assessment with some pointers on how to improve.