10.1 Interpreting rounding errors and estimating answers
You can use the rounding of numbers to estimate the answer to a calculation.
Here are some examples where we can use estimate the answer much quicker than calculating.
We round each number to the nearest 10, 100, 1000 depending on the place value of the first digit.
Pippa sold 684 motorbike racing programmes at £10.49 each.
Using rounding and estimation, the calculation would be:
700 × £10 = £7000
The exact calculation would be: 684 × £10.49 = £7175.16.
Samuel sold 204 limited edition programmes at £14.65.
Using rounding and estimation, the calculation would be:
200 × £15 = £3000
The actual calculation would be: 205 × £14.65 = £3003.25
By using rounding and estimation, you can judge whether your answers are sensible.
Activity 41: Rounding and estimating answers
Liam sold 432 concert tickets at £25.75 each.
Using rounding and estimation, calculate how much he earned and then, by using a calculator, calculate the exact earnings.
Answer
Using rounding and estimation, the calculation would be:
400 × £26=£10,400
The exact calculation would be:
432 × £25.75=£11,124
Rounding errors on a calculator
Sometimes the results on a calculator may have recurring digits which will need to be rounded before further use. For example:
3.99999999: rounded to the whole number, i.e. 4
6.99999999: rounded to the whole number, i.e. 7
0.11111111: rounded to 1 decimal place, i.e. 0.1