# Approximate value

An approximation is mathematics an approximate result for an exact value, as a decimal number as an approximation for the circle constant . Approximate values ​​are often used when the exact calculation is very complex or not possible or only a certain level of accuracy is required or can be represented. It is important to correct the error, i. H. estimate the distance between the exact value and the approximate value against a given value : ${\ displaystyle \ pi}$${\ displaystyle x}$${\ displaystyle a}$${\ displaystyle d}$

${\ displaystyle | ax |

For example, the error bound applies to and . If the calculation is continued with an approximate value instead of the exact value, then this error can increase considerably and error propagation occurs . For this reason, it sometimes makes sense to use the exact values ​​as much as possible and only give an approximate value for the final result. ${\ displaystyle x = \ pi}$${\ displaystyle a = 3 {,} 14}$ ${\ displaystyle | ax | <{\ tfrac {1} {627}}}$

## Examples

The circle number is an irrational number . The exact value (in symbolic or numeric form) is not relevant for most calculations, as only a certain degree of accuracy is required. For a rough rollover, an approximate value is often sufficient, e.g. B.   or   with two decimal places . For more precise calculations, a numerical value can be used for, for example ${\ displaystyle \ pi}$${\ displaystyle \ pi \ approx {\ tfrac {22} {7}},}$   ${\ displaystyle \ pi \ approx {\ sqrt {2}} + {\ sqrt {3}},}$   ${\ displaystyle \ pi \ approx {\ sqrt {10}}}$${\ displaystyle \ pi \ approx 3 {,} 14}$${\ displaystyle \ pi}$${\ displaystyle \ pi = 3 {,} 141592653 \ dotso}$

## literature

• Heidrun Günzel: Ordinary differential equations . Oldenbourg Verlag Munich, Munich 2008, ISBN 978-3-486-58555-1 .
• SE Baltrusch: Outline of elementary arithmetic and algebraic mental arithmetic . Publishing house by Veit and Comp., Berlin 1836.
• Helmuth Gericke: Mathematics in Antiquity and the Orient . Springer Verlag, Berlin 1984, ISBN 978-3-642-68631-3 .