Bounds and error in rounded values

Mathematics · Number Representation & Place Value · ages 12-14

Name ______________________ Date ____________

Estimate 396 + 205 by rounding each number to the nearest hundred, then add.
Answer: ______________
Estimate 19.8 × 5.1 by rounding each number to the nearest whole number first.
- 100
- 95
- 20
- 24
To estimate 58 × 19, which rounded numbers should you multiply?
- 60 × 20
- 50 × 10
- 58 × 19
In 6.5 ≤ x < 7.5, the value 7.5 itself is included in the range.
Circle one: True False
A pencil is measured as 12 cm long, to the nearest cm. What is the upper bound of its actual length, in cm?
Answer: ______________
Which inequality correctly describes a length x that rounds to 9 m to the nearest metre?
- 8 ≤ x < 9
- 8.5 < x < 9.5
- 8.5 ≤ x < 9.5
Estimate 29.6 ÷ 5.9 by rounding each number to the nearest whole number first.
- 5
- 6
- 4
- 30
A length x is recorded as 12 cm, to the nearest cm. Which inequality correctly shows the error interval for x?
- 11.5 ≤ x < 12.5
- 11 ≤ x < 13
- 11.5 < x ≤ 12.5
- 12 ≤ x < 12.5
Priya estimates 8.7 × 4.3 by rounding to 8 × 4 = 32. What did she get wrong?
- She should not round at all
- She rounded 8.7 down to 8, but 8.7 is closer to 9
- 32 is not a whole number
A distance is recorded as 7.2 km, to the nearest tenth of a km. True or false: the error interval is 7.15 ≤ x < 7.25.
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

600 · Rounding to the nearest hundred makes the addition simple.
100 · Rounding first turns a messy multiplication into an easy one.
60 × 20 · 58 rounds up to 60 and 19 rounds up to 20 (nearest ten), giving an easy estimate of 60 × 20.
False · 7.5 would round up to 8, not down to 7, so it sits just outside the range. That's why we use < instead of ≤ at the top end.
12.5 · The upper bound is the largest value that would still round down to 12.
8.5 ≤ x < 9.5 · The bounds are half a unit either side of 9: 8.5 and 9.5. We include the lower bound with ≤ but not the upper bound, since 9.5 m would round up to 10 m.
5 · Rounding both numbers before dividing gives a quick, close estimate.
11.5 ≤ x < 12.5 · The error interval collects every value that would round to 12, using ≤ on the lower side and < on the upper side.
She rounded 8.7 down to 8, but 8.7 is closer to 9 · 8.7 is closer to 9 than to 8, so it should round up. The better estimate is 9 × 4 = 36.
True · Checking both bounds against the rounding rule confirms this interval is correct.