Upper and lower bounds in additive calculations | Maths

Starter quiz

An error interval for a number shows the ______ of possible values of the number.

'range' ✓
Work out the lower and upper bounds of 560 rounded to the nearest 10

559 and 561

559.5 and 560.5

555 and 564

554 and 565

555 and 565 ✓
Work out the lower and upper bounds of 4.8 rounded to 1 decimal place.

4.7 and 4.9

4.75 and 4.85 ✓

4.3 and 5.3

4.74 and 4.85

4.75 and 4.84
______ rounded to the nearest integer. The lower bound is 8.5 and the upper bound is 9.5

'9' ✓
______ rounded to 1 decimal place. The lower bound is 1.65 and the upper bound is 1.75

'1.7' ✓
______ rounded to 2 significant figures. The lower bound is 1250 and the upper bound is 1350

'1300' ✓

The numbers either end of an error interval are called the lower and upper ______.

'bounds' ✓
A piece of string is measured as 10.2 cm correct to 1 decimal place. What are the lower and upper bounds?

9.7 and 10.7

10.25 and 10.35

10.15 and 10.25 ✓

10.15 and 10.24
A piece of string is measured as 10.2 cm correct to 1 decimal place. The lower and upper bounds are 10.15 and 10.25. What is the error interval?

$10.15\leq{x}\leq10.25$

$10.15\leq{x}<10.25$ ✓

$10.15<{x}\leq10.25$

$10.15\geq{x}<10.25$

$10.15\leq{x}>10.25$
The mass of a cat is 4.8 kg correct to 2 significant figures. What is the error interval?

$4.75\leq{x}<7.849999999999$

$4.75\leq{x}<4.85$ ✓

$4.75\leq{x}\leq4.85$

$4.75<{x}<4.85$
Here are the error intervals for $x$ and $y$ : $24.5\leq{x}<25.5$ and $9.5\leq{y}<10.5$ . What are the lower and upper bounds of $x + y$ ?

34 and 35

34 and 36 ✓

35 and 35

35 and 36
Here are the error intervals for $x$ and $y$ : $24.5\leq{x}<25.5$ and $9.5\leq{y}<10.5$ . What are the lower and upper bounds of $x - y$ ?

15 and 16

15 and 15

14 and 15

14 and 16 ✓

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The biggest possible sum comes from adding the upper bounds.
The smallest possible sum comes from adding the lower bounds.
The biggest possible difference comes from subtracting a lower bound from an upper bound.
The smallest possible difference comes from subtracting an upper bound from a lower bound.

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