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Year 8

Inequality notation to express error

I can calculate possible errors expressed using inequality notation a ≤ x < b.

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New
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Year 8

Inequality notation to express error

I can calculate possible errors expressed using inequality notation a ≤ x < b.

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Lesson details

Key learning points

  1. When given a rounded number you can say what the biggest and smallest values of the unrounded number could have been.
  2. 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 or error intervals is used a lot in different industries around the world. Discuss why are error intervals 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

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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6 Questions

Q1.
Which of the following is not an integer?
−3249
10 904
Correct answer: 12 348.4839
Correct answer: 34 839.48
439 043 904
Q2.
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
Q3.
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 = 3950
Smallest integer = 3855, largest integer = 3950
Q4.
When does 0.4999999 NOT round to give 0.5?
Correct answer: 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.
Correct answer: 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.
80.5 cm
805 cm
1255 cm
Correct answer: 5755 cm
12 550 cm

Exit quiz

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6 Questions

Q1.
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: $$ a\leq x < b$$
Q2.
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 = $$8.9 \dot 9$$
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.
Smallest = $$18.5$$, Largest = $$19.5 \dot 9$$
Correct answer: 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 $$x$$.
 $$ 7.5< x < 8.4 \dot 9$$
$$ 7.5> x < 8.4 \dot 9$$
$$ 7.5\leq x < 8.4 \dot 9$$
Correct answer: $$7.5\leq x< 8.5$$
$$7.5 \geq x <8.4 \dot 9$$
Q5.
When a number, $$x$$, is rounded to 2 significant figures the result is 7.8. Identify the error interval for $$x$$.
 $$ 7.75< x < 7.84 \dot 9$$
Correct answer:  $$ 7.75\leq x < 7.85 $$
 $$ 7.74 \dot 9< x < 7.84 \dot 9$$
 $$ 7.75 < x < 7.85 $$
Q6.
A distance $$x$$ km is given as 2.345 km correct to the nearest metre. Identify the error interval for $$x$$.
$$ 2.3445\leq x < 2.3449$$
$$2.3445 \geq x <2.3454 \dot 9$$
$$ 2.3445> x < 2.3454\dot 9$$
 $$ 2.3445< x < 2.3455$$
Correct answer: $$ 2.3445\leq x < 2.3455$$