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Upper and lower bounds calculator

Work out

Error interval for 6.4

6.35 ≤ x < 6.45

Lower bound 6.35, upper bound 6.45.

Working

  1. Rounded to 1 decimal place, the value goes up in steps of 0.1. Half of that is 0.05.
  2. Lower bound = 6.4 − 0.05 = 6.35. Upper bound = 6.4 + 0.05 = 6.45.
  3. Error interval: 6.35 ≤ x < 6.45. The upper bound itself would round up, so it gets "<", not "≤".

Your result

6.35 ≤ x < 6.45. Lower bound 6.35, upper bound 6.45.

Bounds and error intervals

Open the rounding and error intervals lesson

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A value rounded to 1 decimal place can be up to half of 0.1 either side: 6.4 to 1 d.p. has the error interval 6.35 ≤ x < 6.45, with lower bound 6.35 and upper bound 6.45.

Questions people ask

How do you find the upper and lower bounds?

Halve the unit the value was rounded to, then add it for the upper bound and subtract it for the lower bound. 70 to the nearest 10 has bounds 65 and 75.

What is an error interval?

The range of values that round to your number, written lower bound ≤ x < upper bound. The upper bound gets < because it would round up to the next value.

How do you find the upper bound of a division?

Divide the biggest top by the smallest bottom: upper bound of x ÷ y = UB of x ÷ LB of y.

What is the difference between rounding and truncating?

Rounding goes to the nearest value; truncating just cuts the digits off. 6.78 truncated to 1 d.p. is 6.7, so its error interval is 6.7 ≤ x < 6.8.

Keep going

How we work this out

What it does

Find the error interval for a rounded or truncated number, or the upper and lower bounds of a calculation.

Values rounded to decimal places, significant figures or the nearest unit, or truncated; calculations of two rounded values.

Method

  1. Lower bound = value − half the unit; upper bound = value + half the unit. A truncated value can be up to one whole unit above.
  2. Error interval: lower bound ≤ x < upper bound.
  3. Add: UB + UB. Subtract: UB − LB. Multiply: UB × UB. Divide: UB ÷ LB (and the reverse for the lower bound).