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I want to create a rule on finding the upper and lower bound of a number.

Examples:

For $29.8$ (3 s.f.) we write $1$ in the place of the $8$ and zero in every other position, giving us $0.01$. After that we divide $\frac{0.01}{2} = 0.005$ and use that number to add and subtract $29.8$ by, giving us $29.75$ and $29.85$ as the lower and upper bounds, respectively.

For $0.661$ (3 s.f.) we leave the $1$ in its place and zero in every other position, giving us $0.001$. After that we divide $\frac{0.001}{2} = 0.0005$ and use that number to add and subtract $0.661$ by, giving us $0.6615$ and $0.6605$ as the lower and upper bounds, respectively.

My question is why does this method fail on the following question: Find the upper and lower bounds of $1000$ (one s.f.)?

The method would give us $1500$ and $500$ whereas the correct answer is $1500$ and $950$ respectively.

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It fails because your rounded number is a power of $10$

You would for example have a similar issue with $0.0100$ as three significant figures: the bounds would be $0.01005$ and $0.009995$ rather than $0.00995$ (spot the extra $9$)

So your rule needs to check you are starting from a power of $10$. If so, the amount to subtract for the lower bound is a tenth of the amount to add for the upper bound

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