Is there a method to avoid long division?

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Arbitary $4$ digit numbers $a$ and $b$ are given. The object is to calculate the fraction $\frac{a}{b}$ without electronic help and without the usual division method.

The result should be correct until the second digit after the decimal point. Two variants are possible :

  • The second digit is not rounded correctly, the result always gives the first two digits after the decimal point.

  • We always get the number $\frac{a}{b}$, correct rounded to the second digit after the decimal point.

I accept both variants, but the method must always give the result according to the given variant.

A rough approximation would be to round $a$ and $b$ correct to the next hundred, which gives a smaller fraction , but the accuracy is too low in general.

Another approach would be to calculate $\frac{a+x}{b+x}$ , where $x$ is chosen in such a way that $b+x$ is divisble by $100$ or even $1000$, but this approximation is not accurate enough in general either.

Does anyone have a good idea ?