Upper and lower bounds | Maths | Quizalize & Oak National Academy

Starter quiz

In the number 56 392 the 3 is the third ______ figure.

'significant' ✓
Choose the correct calculation to estimate the cost of hiring an electrician for 4.5 hours, where the total cost = £42.50 × number of hours + £25

£50 × 5 + £30

£50 × 5 + £20

£50 × 4 + £30

£40 × 5 + £30 ✓

£40 × 4 + £30
Estimate the value of ${435.8\times8.742\over3.04}$

'1200' ✓
Will the estimation of 128.03 + 0.512 be an overestimate or underestimate?

'overestimate' ✓
Estimate the amount of change received from £500 when purchasing a TV costing £375

'£100' ✓
Estimate the circumference of a circle with a radius of 8.4 cm.

'60 cm' ✓

Upper and lower bounds are used when a number has been ______.

'rounded' ✓
Work out the lower and upper bounds of 320 rounded to the nearest 10

319.5 and 320.5

315 and 324

310 and 330

315 and 325 ✓

310 and 325
Work out the lower and upper bounds of 12.6 rounded to 1 decimal place.

12.7 and 12.9

12.1 and 13.1

12.55 and 12.65 ✓

12.55 and 12.64

12.55 and 12.6499999999999
______ rounded to the nearest integer. The lower bound is 147.5 and the upper bound is 148.5

'148' ✓
______ rounded to 1 decimal place. The lower bound is 10.25 and the upper bound is 10.35

'10.3' ✓
______ rounded to 2 significant figures. The lower bound is 8750 and the upper bound is 8850

'8800' ✓

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When given a rounded number you can say what the biggest and smallest values of the unrounded number could have been .
You can use a ≤ x < b notation to express the range of values the unrounded number could have taken.
You can use those values in your estimate to see what your biggest and smallest answers could have been.
The range of possible answers is the error interval.

For example if a measurement of 12 cm has been given to the nearest centimetre assuming the upper bound is 12.4 cm.

Emphasise the infinite nature of a measurement.

Upper bound - The upper bound for a rounded number is the smallest value that would round up to the next rounded value.
Lower bound - The lower bound for a rounded number is the smallest value that the number could have taken prior to being rounded.
Error interval - An error interval for a number x shows the range of possible values of x. It is written as an inequality a ≤ x < b