Free Maths Calculator

Bounds Calculator

When a value has been rounded, the true number lives in a range. Enter the rounded value and how it was rounded, and get the lower bound, the upper bound and the error interval, with the half-a-step reasoning written out the way the mark scheme wants it.

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    Worked Example

    A length is 240 cm to the nearest 10 cm. What are the bounds?

    1. The rounding step is 10, so anything within half of that, 5, rounds to 240
    2. Lower bound:240 − 5 = 235
    3. Upper bound:240 + 5 = 245, giving the interval 235 ≤ length < 245

    Answer: Lower bound 235 cm, upper bound 245 cm

    Try These Yourself

    A mass is 6.7 kg to 1 decimal place. Bounds?Show answerHide answer

    Answer: 6.65 and 6.75

    Half of 0.1 is 0.05 either side.

    A crowd is 3,000 to the nearest 100. Smallest possible size?Show answerHide answer

    Answer: 2,950

    3,000 − 50.

    x = 15 to the nearest whole number. Error interval?Show answerHide answer

    Answer: 14.5 ≤ x < 15.5

    Half a unit either side, strict at the top.