Rounding is he process and result of rounding (eliminate certain figures or differences to consider a whole unit). Thanks to the rounding process, calculations.
Rounding consists of do not consider decimals, cutting the number to keep only the whole. This means, if we want to round the number 2.3, we will remove the 0.3 and we will keep him two. On the other hand, if the objective is to round 4.9, the rounding mechanism will lead to bypassing the 0.9 and 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 upwards, obtaining a bigger number. While in the first case the rounding will be carried out by eliminating decimals, in the second it will be necessary to add a amount to reach the next whole number.
Rounding is not only used to operate with whole numbers: it can also be used to eliminate some decimal. The number 8.1463 can be rounded as 8,146 or, clipping another decimal, like 8.15.
A concept related to rounding is the truncation, which belongs to numerical analysis (a mathematical subfield) and refers to the technique used to reduce the number of decimal digits, that is, those to the right of the separator, which can be a comma or a period, depending on the country. As demonstrated in the previous paragraph, through truncation a number such as 8.1463 can happen to be 8,146 if you want truncate it to three decimal digits.
Rounding is common in the field of commerce, either to facilitate transactions or to make up for the lack of coins that allow a payment that is too exact. Suppose a person acquire different products in a store and the bill to pay is 48.97 pesos. To facilitate payment, rounding can be done at 49 pesos. In this way, the return of the change is facilitated (the rest, also known as return or change).
It should be noted that, in some countries, there are laws that rounding must be in favor of the buyer. Returning to the last example, if the seller wants to round since he does not have coins to deliver the change, 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 according to the conventions. Let’s see an example for each of them, in which we will always have the objective of rounding a number to its hundredths, that is, leaving it only two decimal digits:
* rule 1: if the next digit to the right after the last one that 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 Unit. For example: 8,459 would become 8.46;
* rule 3: If a 5 follows the last digit you want to keep and after 5 there is at least one number other than 0, the last must be increased by one. 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 is done changes than mere truncation. For example, 4.32500 Y 4,325 would become 4.32;
* rule 5– Opposite to the previous rule, if the last required digit is an odd number, then we need to increase it by one. For example: 4.31500 Y 4,315 would become 4.32.