Write Upper and Lower Bounds Using Intervals

Finding upper and lower bounds when rounding numbers shows us where an actual value of a rounded number can lie between.

 

Suppose we have a number that has been rounded to the nearest 10 and got 20, the numbers that could round up to give 20 include:

15, 16, 17 , 18, 19

The smallest value the number can be is 15. This is the lower bound.

 

The numbers larger than 20 that could round down to 20 include:

21, 22, 23, 24

The largest value that could round down to 20 would be 24.999999...

This means that the upper bound would be 25. It includes all numbers up to but not including 25.

 

We could write this using inequalities or intervals.

15 ≤ x < 25

The value of x is greater than or equal to 15 and up to but not including 25.

 

Example

A value has been rounded to 200 to the nearest 100.

Write the interval for the upper and lower bounds for the rounded value.

 

First, let's find half of the rounded unit.

100 ÷ 2 = 50 

 

Upper bound = 200 + 50 = 250

Lower bound = 200 - 50 = 150

 

The interval can then be written as:

150 ≤ x < 250

 

Are you happy with that?

 

 

Let's get started.