# Irrational number approximation by a rational number

1. May 20, 2010

### n.karthick

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.

2. May 20, 2010

### Xitami

best rational approximation (via continued fractions)

3. May 20, 2010

### mathman

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.

4. May 20, 2010

### lurflurf

^That tends to give big denominators, how distasteful.

5. May 21, 2010

### mathman

Most of the time you can't do much else.

6. May 21, 2010

### Count Iblis

7. Jun 21, 2010

### Abu Rehan

Write down the decimal expansion to the accurate number of digits required+1 and make the penultimate digit to round figure and then convert it to fraction by dividing it by 10 to power number of decimal digits.