1. Approximation Objectives for today’s lesson :
Practice Upper & Lower Bounds
Using Rounding appropriately
Finding bounds on answers

2. Starter
In pairs, try and find pairs of numbers which are the same when rounded to :
1 decimal place and 2 significant figures
3 dp’s and 7 sf’s

3. Upper & Lower bounds
Find the upper & lower bounds of these numbers which are rounded to 2 significant figures :
Lower Upper 99
140 10
1100
0.035

4. Upper & Lower bounds
Find the upper & lower bounds of these numbers which are rounded to 2 significant figures :
Lower Upper
140 10
1100
0.035

5. Upper & Lower bounds
Find the upper & lower bounds of these numbers which are rounded to 2 significant figures :
Lower Upper 10
1100
0.035

6. Upper & Lower bounds
Find the upper & lower bounds of these numbers which are rounded to 2 significant figures :
Lower Upper
1100
0.035

7. Upper & Lower bounds
Find the upper & lower bounds of these numbers which are rounded to 2 significant figures :
Lower Upper
0.035

8. Upper & Lower bounds
Find the upper & lower bounds of these numbers which are rounded to 2 significant figures :
Lower Upper

9. Notation The best notation to use for upper & lower bounds is this :
If a number (say x) is 42 when rounded to 2 sf’s, then ……
41.5 ≤ x < 42.5
The lower bound = The upper bound = 42.5
No equals sign
x could equal 41.5

10. Using rounding appropriately
Example The height of 4 people is measured to 3 sf’s (in cm) :
Calculate the mean.

11. Using rounding appropriately
The mean is ( ) / 4 =

12. Using rounding appropriately
The mean is ( ) / 4 =
However, as the data was rounded to 3sf’s, it is appropriate to do the same with the answer.

13. Using rounding appropriately
The mean is ( ) / 4 =
However, as the data was rounded to 3sf’s, it is appropriate to do the same with the answer.
So the mean is 152 cm.

14. Finding bounds on answers
Example
A rectangle is measured as follows :
What are the biggest
and smallest possible
values for the area?
24cm ± 0.5cm
16cm ± 0.5cm

15. Finding bounds on answers
Biggest value = x 16.5 =
Smallest value = x 15.5 =
Therefore :
≤ Area <

16. Question Practice
All on page 238
Q1 parts a to d only Q2
Extension Q3