Inequality notation to express error | Maths | Quizalize & Oak National Academy

Starter quiz

Which of the following is not an integer?

−3249

10 904

12 348.4839 ✓

34 839.48 ✓

439 043 904
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

Smallest integer = 515, largest integer = 524 ✓
State the smallest and largest integers that round to 3900 when rounded to the nearest 100.

Smallest integer = 3849, largest integer = 3949

Smallest integer = 3850, largest integer = 3949 ✓

Smallest integer = 3850, largest integer = 3950

Smallest integer = 3855, largest integer = 3950
When does 0.4999999 NOT round to give 0.5?

When rounded to the nearest integer. ✓

When rounded to 1 significant figure.

When rounded to 1 decimal place.
Work out 3.4 km + 348 m + 6000 cm. Give your answer in metres.

3808 m ✓

380.8 m

38.08 m

4 348 m

434.8 m
Work out 0.05 km + 6.32 m + 123 cm. Give your answer in centimetres.

80.5 cm

805 cm

1255 cm

5755 cm ✓

12 550 cm

Exit quiz

An error interval for a number $x$ shows the range of possible values of $x$ . It is written as:

$a< x < b$

$a> x < b$

$a \geq x$

$a\leq x < b$ ✓
When a number is rounded to the nearest integer the result is 8. Identify the correct range for the unrounded number.

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 = $8.5$
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 = $19.5 \dot 9$

Smallest = $18.5$ , Largest = $19.4 \dot 9$ ✓

Smallest = $17.5$ , Largest = $19.5$

Smallest = $18.5$ , Largest = $19.5$
When a number, $x$ , is rounded to the nearest integer the result is 8. Identify the error interval for $x$ .

$7.5< x < 8.4 \dot 9$

$7.5> x < 8.4 \dot 9$

$7.5\leq x < 8.4 \dot 9$

$7.5\leq x< 8.5$ ✓

$7.5 \geq x <8.4 \dot 9$
When a number, $x$ , is rounded to 2 significant figures the result is 7.8. Identify the error interval for $x$ .

$7.75< x < 7.84 \dot 9$

$7.75\leq x < 7.85$ ✓

$7.74 \dot 9< x < 7.84 \dot 9$

$7.75 < x < 7.85$
A distance $x$ km is given as 2.345 km correct to the nearest metre. Identify the error interval for $x$ .

$2.3445\leq x < 2.3449$

$2.3445 \geq x <2.3454 \dot 9$

$2.3445> x < 2.3454\dot 9$

$2.3445< x < 2.3455$

$2.3445\leq x < 2.3455$ ✓

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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.

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.

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 $a ≤ x < b$