Upper and Lower Bounds for Approximation

This video tutorial explains the concept of upper and lower bounds in approximation, particularly when numbers are rounded. It covers how to determine these bounds, using examples to illustrate the range within which the actual value of a rounded number can fall. The video also discusses the effect of rounding to different units and provides practice questions for viewers to test their understanding.

What is the purpose of identifying upper and lower bounds when a number is rounded?

• To calculate the average of the possible values

• To identify errors in rounding

• To find the range within which the actual value could lie

• To determine the exact value of the number

If a number is rounded to the nearest whole number, what is the lower bound for the number 9?

• 9.5

• 9.0

• 8.5

• 8.0

Why can't the actual value be equal to the upper bound?

• Because it would round to the next higher number

• Because it is always less than the lower bound

• Because it is an arbitrary limit

• Because it is equal to the lower bound

When rounding to the nearest 100, how much larger or smaller can the actual value be?

• Up to 25 units

• Up to 10 units

• Up to 100 units

• Up to 50 units

What should you do after watching the examples in the video?

• Skip to the next video

• Pause and try the practice questions

• Take notes on the examples

• Rewatch the entire video