Topics › KS4 › Number · Foundation & Higher
Error intervals & bounds
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A length, $l$ cm, is $7$ cm correct to the nearest centimetre. Which is the error interval for $l$?
A
Option A:
$6.5 < l \le 7.5$
B
Option B:
$6 \le l < 8$
C
Option C:
$6.5 \le l \le 7.4$
D
Option D:
$6.5 \le l < 7.5$
Answer and misconceptions
A
Option A:
$6.5 < l \le 7.5$
✗
Puts the inequality signs the wrong way round$6.5$ rounds up to $7$, so it is included ($\le$); $7.5$ rounds up to $8$, so it is not ($<$).
B
Option B:
$6 \le l < 8$
✗
Goes a whole unit either sideUses $7 \pm 1$; the bounds are half a unit either side: $7 \pm 0.5$.
C
Option C:
$6.5 \le l \le 7.4$
✗
Uses the largest 1 d.p. value that rounds to $7$ as the upper boundValues such as $7.45$ also round to $7$. The upper bound is $7.5$, written with $<$ because $7.5$ itself is not included.
D
Option D:
$6.5 \le l < 7.5$
✓ Correct
-
The mass of a parcel is $340$ g, correct to the nearest $10$ g. What is the lower bound of the mass?
A
Option A:
$339.5$ g
B
Option B:
$335$ g
C
Option C:
$330$ g
D
Option D:
$345$ g
Answer and misconceptions
A
Option A:
$339.5$ g
✗
Always takes off $0.5$Uses half of $1$; the mass is rounded to the nearest $10$ g, so take off half of $10$ g, which is $5$ g.
B
Option B:
$335$ g
✓ Correct
C
Option C:
$330$ g
✗
Takes off the whole unit of roundingWorks out $340 - 10$; the lower bound is half a unit below: $340 - 5$.
D
Option D:
$345$ g
✗
Gives the upper bound instead of the lower boundWorks out $340 + 5$; the lower bound is the smallest value that rounds to $340$.
-
A number $x$ is truncated to 1 decimal place. The result is $4.3$. Which is the error interval for $x$?
A
Option A:
$4.3 \le x < 4.4$
B
Option B:
$4.25 \le x < 4.35$
C
Option C:
$4.2 < x \le 4.3$
D
Option D:
$4.3 \le x \le 4.39$
Answer and misconceptions
A
Option A:
$4.3 \le x < 4.4$
✓ Correct
B
Option B:
$4.25 \le x < 4.35$
✗
Treats truncating as roundingTruncating chops off the extra digits, so $4.39$ truncates to $4.3$ but $4.25$ truncates to $4.2$.
C
Option C:
$4.2 < x \le 4.3$
✗
Thinks truncating rounds upTruncating never makes a number bigger, so $x$ is $4.3$ or a little more, not a little less.
D
Option D:
$4.3 \le x \le 4.39$
✗
Uses the largest 2 d.p. value as the upper boundValues such as $4.395$ also truncate to $4.3$. The upper bound is $4.4$, written with $<$ because $4.4$ itself truncates to $4.4$.
-
A number $n$ is $3600$ when rounded to 2 significant figures. Which is the error interval for $n$?
A
Option A:
$3595 \le n < 3605$
B
Option B:
$3500 \le n < 3700$
C
Option C:
$3550 \le n < 3650$
D
Option D:
$3599.5 \le n < 3600.5$
Answer and misconceptions
A
Option A:
$3595 \le n < 3605$
✗
Treats 2 significant figures as the nearest $10$The 2nd significant figure of $3600$ is the $6$, in the hundreds column, so $n$ was rounded to the nearest $100$.
B
Option B:
$3500 \le n < 3700$
✗
Goes a whole unit either sideUses $3600 \pm 100$; the bounds are half a unit either side: $3600 \pm 50$.
C
Option C:
$3550 \le n < 3650$
✓ Correct
D
Option D:
$3599.5 \le n < 3600.5$
✗
Treats 2 significant figures as the nearest whole numberUses $\pm 0.5$; $3600$ to 2 significant figures means the nearest $100$, so use $\pm 50$.
-
A length is $2.4$ m, correct to 1 decimal place. What is the upper bound of the length?
A
Option A:
$2.44$ m
B
Option B:
$2.5$ m
C
Option C:
$2.9$ m
D
Option D:
$2.45$ m
Answer and misconceptions
A
Option A:
$2.44$ m
✗
Thinks the upper bound must round to the given valueValues such as $2.449$ also round to $2.4$. The upper bound is $2.45$, even though $2.45$ itself would round up.
B
Option B:
$2.5$ m
✗
Adds the whole unit of roundingAdds $0.1$; the upper bound is half of $0.1$ above: $2.4 + 0.05$.
C
Option C:
$2.9$ m
✗
Always adds $0.5$Adds half of $1$; the length is rounded to the nearest $0.1$ m, so add half of $0.1$, which is $0.05$.
D
Option D:
$2.45$ m
✓ Correct