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 these bounds define the range within which the actual value of a rounded number can fall. The tutorial provides examples, explaining that the lower bound is the smallest value that rounds to the estimated value, while the upper bound is the smallest value that rounds up to the next estimated value. The video also includes practice questions to reinforce understanding.

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

• To calculate the average of the rounded number

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

• To identify errors in rounding

• 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?

• 9.0

• 8.5

• 9.5

• 8.0

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

• Because it is equal to the lower bound

• Because it is an arbitrary limit

• Because it is always less than the lower bound

• Because it would round to the next higher number

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

• Up to 10 units

• Up to 100 units

• Up to 25 units

• Up to 50 units

What happens to the actual value when a number is rounded to a unit?

• It is always less than the lower bound

• It can be exactly equal to the rounded number

• It becomes an exact multiple of the unit

• It can be up to half a unit larger or smaller