Using inequality notation for errors in calculations | Maths

Starter quiz

An error interval for a number $x$ shows the range of possible values of $x$ . It is written as $a\leq x < b$ . Explain what this means.
- The range of values include $a$ and $b$
- The range of values include $a$ and not $b$ ✓
- The range of values includes all the numbers strictly in between $a$ and $b$
- The range of values do not include $a$ but include $b$
When a number, $x$ , is rounded to the nearest integer the result is 63. Select the numbers which complete the error interval for $x$ : $\square \leq x <\square$
- 62.5 and 65.5
- 63.5 and 64.5
- 62.5 and 64.5
- 62.5 and 63.5 ✓
When a number, $x$ , is rounded to the nearest integer the result is 5. Select the numbers which complete the error interval for $x$ : $\square \leq x <\square$
- 4.5 and 5.6
- 4.5 and 5.5 ✓
- 3.5 and 6.5
- 4.5 and 5.49
When a number, $x$ , is rounded to the nearest integer the result is 10. Select the numbers which complete the error interval for $x$ : $\square \leq x <\square$
- 9.5 and 10.4999
- 5 and 14.5
- 5 and 14.49999
- 9.5 and 10.5 ✓
Jun rounds a number to the nearest integer and the result is 5. Izzy rounds a number to 1 d.p. and the result is 5.0. Jun says, "We must both have rounded the same number." Is Jun correct?
- Jun is correct as both are the same when rounded to 1 d.p
- Jun is correct as both values will be the same when inputting into a calculator.
- Jun is incorrect as they have different error intervals. ✓
$x$ and $y$ are both integers. $x$ = 650 (rounded to the nearest 10) and $y$ = 800 (rounded to the nearest 100). The greatest possible integer value of $x+y$ is ______.
- '1503' ✓

Exit quiz

__________ are the digits in a number that contribute to the accuracy of the number. The first significant figure is the first non-zero digit.
- Estimated numbers
- Important numbers
- Real numbers
- Significant figures ✓
When a number, $x$ , is rounded to the nearest integer the result is 35. Select the numbers which complete the error interval for $x$ : $\square \leq x <\square$
- $35$ and $45$
- $34.5$ and $35.5$ ✓
- $34.999$ and $35.999$
- $34.4 \dot 9$ and $35.4 \dot 9$
A long road is made up of 3 sub roads. The 1st road measures 35 m (2 s.f), the 2nd road is 41 m (2 s.f) and the 3rd road is 48 m (2 s.f). Find the error interval for the length $x$ of the long road.
- $122.5 \leq x < 125.5$ ✓
- $122 \leq x < 125$
- $122.5 \leq x < 125.59$
- $124.5 \leq x < 126.5$
A wall is in an L-shape. All the lengths are given to 1 d.p or the nearest integer. Work out the error interval for the area of the wall.
- $19.6375 \leq x < 22.7875$
- $18 \leq x <23$
- $18.96 \leq x <20.96$
- $18.7875 \leq x <23.6375$ ✓
A square has lengths in cm given to 1 decimal place. The error interval of the perimeter of the square is $31 \leq x <31.4$ . Work out the length of the square correct to 1 d.p.
- 7.2
- 7.4
- 7.6
- 7.8 ✓
- 8.0
A square has lengths in cm to 1 decimal place. The error interval of the area of the square is $30.8025 \leq x <31.9225$ . Work out the length of the square to 1 d.p.
- 5.5 cm
- 5.4 cm
- 5.6 cm ✓
- 5.8 cm
- 5.3 cm

Worksheet

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Lesson Details

Key learning points

You can use the values of a and b to see what the biggest and smallest answers to a calculation could have been.
The range of possible answers is the error interval.

Common misconception

When subtracting or dividing, the largest value is found by subtracting or dividing the upper limit of a number by the upper limit of the divisor or additive inverse.

Drawing a number line to show with subtraction will help students see how to achieve an upper or lower limits of an error interval calculation. When using division, reiterating the division of number is the same as multiplying by its reciprocal.

Keywords

Error interval - An error interval for a number $x$ shows the range of possible values of $x$ . It is written as an inequality $a ≤ x < b$