Rounding is the process and the result of rounding (eliminate certain figures or differences to consider an entire unit). Thanks to the rounding process, the calculations .
Rounding consists of don't consider decimals , cutting the number to stay only with the whole . This means, if we want to round the number 2,3 , we will eliminate the 0,3 and we will stay with him 2 . Instead, if the goal is to round 4,9 , the rounding mechanism will lead to set aside the 0,9 and to add 0.1 to be able to work with the number 5 .
With these examples we can see that rounding can be done downwards, reaching a minor number , or up, getting a bigger number . While in the first case the rounding will be carried out eliminating decimals, in the second one will have to add a quantity to reach the next whole number.
Rounding is not only used to operate with integers: it can also be used to eliminate any decimal. The number 8,1463 can be rounded as 8,146 or, by cutting another decimal, such as 8,15 .
A concept related to rounding is the truncation , which belongs to the numerical analysis (a mathematical subfield) and refers to the technique used to reduce the number of decimal digits, that is, those that are to the right of the separator, which can be a comma or a period, depending on the country. As shown in the previous paragraph, through truncation a number such as 8,1463 can happen to be 8,146 if desired truncate it to three decimal digits .
Rounding is common in the field of commerce, either to facilitate transactions or to replace the lack of currencies that allow too exact payment. Suppose a person acquires different products in a store and the bill to pay is 48.97 pesos . To facilitate payment, rounding can be done on 49 pesos . This facilitates the return of the return (the rest, also known as return or change).
It should be noted that, in some countries , there are laws that rounding should be in favor of the buyer. Returning to the last example, if the seller wishes to round since he does not have coins to deliver the return, he will have to do so at 48,95 or 48,90 .
Although many people familiar with mathematics use their intuition when rounding a number, there are five rules well defined that must be respected if you want to proceed in accordance with the conventions. Let's look at an example for each of them, in which we will always have the objective of rounding a number to its hundredths, that is, leaving only two decimal digits:
* rule 1 : If the next digit to the right after the last one you want to keep is less than 5, then the last one should not be modified. For example: 8,453 would become 8,45 ;
* rule 2 : in the opposite case to the previous one, when the digit following the limit is greater than 5, the last one must be increased by one unity . For example: 8,459 would become 8,46 ;
* rule 3 : If a 5 follows the last digit that you want to keep and after 5 there is at least a different number from 0, the last one must be increased by one unit. For example: 6,345070 would become 6,35 ;
* rule 4 if the last desired digit is an even number and to its right there is a 5 as the final digit or followed by zeros, then no more are done changes than mere truncation. For example, 4,32500 and 4,325 would become 4,32 ;
* rule 5 : opposite to the previous rule, if the last digit required is an odd number, then we must increase it by one unit. For example: 4,31500 and 4,315 they would become 4,32 .