# Approximation by Truncation

## Approximation by Truncation

The process of replacing a number with an approximate value found by removing all of the digits from the fractional part that is located to the right of a given position.

The retained part is called the truncation. All of the digits in a truncation are exact digits.

### Example

• Imagine a baseball game in a packed stadium. Knowing that the stadium can contain 33 250 spectators and that it is about two-thirds full, a sports commentator could say that there were more than 22 000 spectators present at this game by proceeding like this: to calculate the thirds, he would use 33 000 instead of 33 250, then because the third, by approximation after having truncated 33 250 to the thousands position to get 33, is 11, so two-thirds would be 22; hence 22 000 spectators. Knowing that he used a value that is less than the real capacity of the stadium, he would say, “more than…”
• The value 3.14 is a truncation of the real value of the constant π. The number 3.1416 is a rounded number of the number π.
• We often use the value 0.666 to designate $$\frac{2}{3}$$. This is a truncation and not a rounded number.