Bounds and error in rounded values · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Bounds and error in rounded values

Mathematics · Number Representation & Place Value · ages 12-14
Name ______________________   Date ____________

  1. A mass is recorded as 12 kg to the nearest kg. What is the lower bound?

    • 11 kg
    • 11.5 kg
    • 12.5 kg

  2. To estimate 58 × 19, which rounded numbers should you multiply?

    • 60 × 20
    • 50 × 10
    • 58 × 19

  3. In 6.5 ≤ x < 7.5, the value 7.5 itself is included in the range.

    Circle one:   True   False

  4. A plank is measured as 154 cm to the nearest cm. Which pair gives the correct bounds?

    • 153 cm and 155 cm
    • 153.5 cm and 154.5 cm
    • 154 cm and 155 cm

  5. Estimate 212 × 48 by rounding each number to the nearest ten, then multiplying. What estimate do you get?

    Answer: ______________

  6. 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

  7. A rectangle's sides are measured as 9 cm and 6 cm, both to the nearest cm. Using the upper bounds (9.5 cm and 6.5 cm), what is the largest possible area?

    Answer: ______________

  8. 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
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Answer key

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

Bounds and error in rounded values W1-mt_VVn1IXjkzn-s1

  1. 11.5 kg · The lower bound is half a kilogram below 12, so 11.5 kg. Anything less would have rounded down to 11 kg.
  2. 60 × 20 · 58 rounds up to 60 and 19 rounds up to 20 (nearest ten), giving an easy estimate of 60 × 20.
  3. 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.
  4. 153.5 cm and 154.5 cm · Half a centimetre either side of 154 gives bounds of 153.5 cm and 154.5 cm.
  5. 10500 · Round 212 to the nearest ten (210) and 48 to the nearest ten (50), then multiply: 210 × 50 = 10500.
  6. 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.
  7. 61.75 · Using the largest possible sides, 9.5 cm and 6.5 cm, the biggest possible area is 9.5 × 6.5 = 61.75 cm².
  8. 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.
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