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Inequality notation to express error
I can calculate possible errors expressed using inequality notation a ≤ x < b.
Lesson 14 of 16
New
New
- Year 8
Inequality notation to express error
I can calculate possible errors expressed using inequality notation a ≤ x < b.
Lesson details
Key learning points
- 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.
Keywords
Range - A range of values where every value in the range estimates to the given value.
Error interval - An error interval for a number $$x$$ shows the range of possible values of $$x$$. It is written as an inequality $$a ≤ x < b$$
Common misconception
Incorrect use of the error interval i.e $$a ≤ x ≤ b$$ or writing the error interval as $$a ≤ x > b$$
As a check, encourage students to round the upper limit interval by the degree of accuracy to see if it evaluates to the rounded number. Also, draw a number line to show the meaning of $$a ≤ x > b$$ and allow students to see the error.
The use of error intervals is used a lot in different industries around the world. Discuss why error intervals are so important. E.g If 5 m has been rounded to the nearest integer, why is it important to know that the actual measurement could have been 4.5 m? Why is it such a big deal?
Teacher tip
Equipment
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Which of the following is not an integer?
Which of the following is not an integer?
−3249
10 904
Correct answer: 12 348.4839
12 348.4839
Correct answer: 34 839.48
34 839.48
439 043 904
Q2.State the smallest and largest integers that round to 520 when rounded to the nearest 10.
State the smallest and largest integers that round to 520 when rounded to the nearest 10.
Smallest integer = 514, largest integer = 525
Smallest integer = 514, largest integer = 524
Smallest integer = 515, largest integer = 525
Correct answer: Smallest integer = 515, largest integer = 524
Smallest integer = 515, largest integer = 524
Q3.State the smallest and largest integers that round to 3900 when rounded to the nearest 100.
State the smallest and largest integers that round to 3900 when rounded to the nearest 100.
Smallest integer = 3849, largest integer = 3949
Correct answer: Smallest integer = 3850, largest integer = 3949
Smallest integer = 3850, largest integer = 3949
Smallest integer = 3850, largest integer = 3950
Smallest integer = 3855, largest integer = 3950
Q4.When does 0.4999999 NOT round to give 0.5?
When does 0.4999999 NOT round to give 0.5?
Correct answer: When rounded to the nearest integer.
When rounded to the nearest integer.
When rounded to 1 significant figure.
When rounded to 1 decimal place.
Q5.Work out 3.4 km + 348 m + 6000 cm. Give your answer in metres.
Work out 3.4 km + 348 m + 6000 cm. Give your answer in metres.
Correct answer: 3808 m
3808 m
380.8 m
38.08 m
4 348 m
434.8 m
Q6.Work out 0.05 km + 6.32 m + 123 cm. Give your answer in centimetres.
Work out 0.05 km + 6.32 m + 123 cm. Give your answer in centimetres.
80.5 cm
805 cm
1255 cm
Correct answer: 5755 cm
5755 cm
12 550 cm
Assessment exit quiz
6 Questions
Q1.An error interval for a number $$x$$ shows the range of possible values of $$x$$. It is written as:
An error interval for a number $$x$$ shows the range of possible values of $$x$$. It is written as:
$$ a< x < b$$
$$ a> x < b$$
$$a \geq x <b$$
Correct answer: $$ a\leq x < b$$
$$ a\leq x < b$$
Q2.When a number is rounded to the nearest integer the result is 8. Identify the correct range for the unrounded number.
When a number is rounded to the nearest integer the result is 8. Identify the correct range for the unrounded number.
Correct answer: Smallest = $$7.5$$, Largest = $$8.4 \dot 9$$
Smallest = $$7.5$$, Largest = $$8.4 \dot 9$$
Smallest = $$7.5$$, Largest = $$8.9 \dot 9$$
Smallest = $$7.5$$, Largest = $$8.5 \dot 9$$
Smallest = $$7.5$$, Largest = $$8.5$$
Q3.When a number is rounded to the nearest integer the result is 19. Identify the correct range for the unrounded number.
When a number is rounded to the nearest integer the result is 19. Identify the correct range for the unrounded number.
Smallest = $$18.5$$, Largest = $$19.5 \dot 9$$
Correct answer: Smallest = $$18.5$$, Largest = $$19.4 \dot 9$$
Smallest = $$18.5$$, Largest = $$19.4 \dot 9$$
Smallest = $$17.5$$, Largest = $$19.5$$
Smallest = $$18.5$$, Largest = $$19.5$$
Q4.When a number, $$x$$, is rounded to the nearest integer the result is 8. Identify the error interval for $$x$$.
When a number, $$x$$, is rounded to the nearest integer the result is 8. Identify the error interval for $$x$$.
$$ 7.5< x < 8.4 \dot 9$$
$$ 7.5> x < 8.4 \dot 9$$
$$ 7.5\leq x < 8.4 \dot 9$$
Correct answer: $$7.5\leq x< 8.5$$
$$7.5\leq x< 8.5$$
$$7.5 \geq x <8.4 \dot 9$$
Q5.When a number, $$x$$, is rounded to 2 significant figures the result is 7.8. Identify the error interval for $$x$$.
When a number, $$x$$, is rounded to 2 significant figures the result is 7.8. Identify the error interval for $$x$$.
$$ 7.75< x < 7.84 \dot 9$$
Correct answer: $$ 7.75\leq x < 7.85 $$
$$ 7.75\leq x < 7.85 $$
$$ 7.74 \dot 9< x < 7.84 \dot 9$$
$$ 7.75 < x < 7.85 $$
Q6.A distance $$x$$ km is given as 2.345 km correct to the nearest metre. Identify the error interval for $$x$$.
A distance $$x$$ km is given as 2.345 km correct to the nearest metre. Identify the error interval for $$x$$.
$$ 2.3445\leq x < 2.3449$$
$$2.3445 \geq x <2.3454 \dot 9$$
$$ 2.3445> x < 2.3454\dot 9$$
$$ 2.3445< x < 2.3455$$
Correct answer: $$ 2.3445\leq x < 2.3455$$
$$ 2.3445\leq x < 2.3455$$
