## Irrational number approximation by a rational number

Is there a way ( a theorem ) to find a rational number for a given irrational number such that it is an approximation to it to the required decimal places of accuracy. For example 22/7 is an approximate for pi for 2 decimal places.
 best rational approximation (via continued fractions)
 Recognitions: Science Advisor There is always the trivial solution. Write out the decimal expansion for the irrational to the required number (plus one) of places. Then truncate (or round). This rational number will satisfy the criterion.

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## Irrational number approximation by a rational number

^That tends to give big denominators, how distasteful.

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