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Maths

Rounding and estimating

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Upper and Lower Bounds

If we are told that a piece of wood is 12cm long to the nearest cm, then what is the range of possible lengths it could be?

It must be at least 11.5cm long to round up to 12cm. But it must be less than 12.5cm, to round down to 12cm. If it was 12.5cm or more we would round up to 13cm.

Since 12.5cm is the upper limit we call this the 'upper bound'.

So we say that 11.5cm is the lower bound and 12.5cm is the upper bound for the length of the piece of wood.

Try these questions.

Question

A fence is 22m long to the nearest metre. What are the upper and lower bounds?

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Answer

The lower bound is 21.5m and the upper bound is 22.5m

Question

A box is 8.5cm wide measured to the nearest tenth of a cm. What are the upper and lower bounds?

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Answer

Anything above 8.45cm will round up to 8.5 to the nearest tenth of a cm.

Anything less than 8.55cm will round down to 8.5cm

The lower bound is 8.45cm and the upper bound is 8.55cm

Now try a Test Bite: Foundation or Higher.

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