Tutor’s Toolkit: Application of Number

Interpreting Information

I4	Estimate amounts and proportions

Useful Web Links:

BBC Bitesize Revision: Maths: Approximating and estimating
http://www.bbc.co.uk/schools/gcsebitesize/maths/numberf/approximatingandestimatingrev1.shtml

I4.1	Accuracy

Scope: 

Students need to be able to:
•	Round quantities to the nearest whole amount.

What students need to know:

We always state amounts and the results of calculations to an appropriate level of accuracy.
If you bought a pack of 7 games for £44.90, how much do they cost each?
On a calculator, you would work this out as 44.90  7 = 6.414285714.
However, telling someone they cost £6. 414285714 would just sound daft!

To the nearest penny is normal with money – that’s £6.41.
We could tell them to the nearest 10p. That’s £6.40.
The nearest pound is £6.
It just depends how accurate we want to be.

The only issue with accuracy is to decide when to round up. There is a convention that the half way point counts as the one above. 
So, the nearest pound to £6.50 is £7.
The nearest 10p to 75p is 80p.

For information on rounding to a given number, decimal places or significant figures, refer to 
Interpreting Information, Section I2

I4.1	Approximate calculation

Scope: 

Students need to be able to:
•	Estimate the outcome of a calculation by rounding to one significant figure.

What students need to know:

Very often we don’t need to know an exact answer to a calculation. Getting a rough idea is fine. This can sometimes be helpful to check that accurate answers are reasonable (refer to Carrying Out Calculations, Section C11).

We normally take only the most significant digit in each number and make a mental calculation.

For example:

27.967  5.2613
This is roughly 30  5 = 150.
If we were asked to estimate the value of the calculation, an answer of 150 would do fine.

Another example:

This is roughly .
In other words, 3  60 then divide by 30.
That’s 180  30 = 6.