# Video: AQA GCSE Mathematics Higher Tier Pack 4 β’ Paper 2 β’ Question 9

Martin measures the length of a shelf that he wants to put up in his living room. The length, π, of the shelf is 82 cm to the nearest centimetre. Write down the error interval that results from rounding.

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### Video Transcript

Martin measures the length of a shelf that he wants to put up in his living room. The length, π, of the shelf is 82 centimetres to the nearest centimetre. Write down the error interval that results from rounding.

The error interval represents the range of values that a number could have been before rounding. Letβs consider a number line. If 82 centimetres is what the result was after rounding to the nearest centimetre, if a value is halfway between 81 and 82, that value is rounded up. Halfway between 81 and 82 is 81.5, 81 and a half, anything greater than or equal to. The values between 81 and a half and 82 all round to 82 centimetres. And that also tells us that anything that equals 82 and a half rounds up to 83.

But what about the values between 82 and 82 and a half? These values round down to 82. We can write this in the form of an inequality. We let π be the length of the shelf. It could be any value greater than or equal to 81 and a half, but less than 82 and a half.

We can read the inequality like this. 81 and a half centimetres is less than or equal to π, the length of the shelf, which is less than 82 and a half centimetres. We can also say that rounding to the nearest centimetre is plus or minus a half a centimetre. 82 minus a half gives the lower bound, and 82 plus one-half gives the upper bound.

And then you have to remember that when dealing with the lower bound, itβs equal to or greater than, while the upper bound is only less than, not equal to.