Bounds and error intervals

Every rounded measurement hides a range of possible true values. Explore lower and upper bounds, then see how they stretch a calculated area.

Curriculum rangeYears 7-11

A measurement is recorded as 23 cm, correct to the nearest whole number.

Measured value23 cm

\text{Lower bound} = 23 - 0.5 = 22.5

\text{Upper bound} = 23 + 0.5 = 23.5

22.5 \leq \text{true value} < 23.5

Learning notes

Bounds and error intervals essentials

Keep these rules beside you while you explore and practise.

1Rounding creates uncertainty

Any rounded measurement could really be anywhere within half a unit either side of the value you were given.

2Lower and upper bounds

\text{lower bound} = \text{value} - \tfrac{1}{2}\times\text{precision}

\text{upper bound} = \text{value} + \tfrac{1}{2}\times\text{precision}

3Error interval

Write the true value as sitting between the two bounds. The lower bound is included; the upper bound is not, because rounding up to it would round to the next value instead.

4Bounds in a calculation

To find the biggest possible answer, use every upper bound; to find the smallest possible answer, use every lower bound.

💡For a division, like speed = distance ÷ time, the maximum answer uses the upper bound on top and the lower bound on the bottom -- not both upper bounds.