Numbers are a really complex world that require deep knowledge to perform mathematical operations correctly without making mistakes that could ruin the final result. For this reason, when carrying out the most basic operations, one usually begins with the natural numbers. Addition is learned almost at the same time as counting. However, all the operations are really variable and, therefore, you have to study step by step to be able to solve them correctly.
In this sense, when one learns to add with natural and real numbers, later it is done with the fractions and finally the decimals are added. Therefore, to reach the last step it is necessary to internalize well the sums with natural numbers.
What are decimal numbers?
When we learn to count, we use units as the most basic element. We count one, two, three, four, five, six, seven, eight, nine, ten, and so on. All these numbers, which are known as the natural numbers, can be represented on an infinite line of values. However, what are known as decimal numbers are the small parts of the unit that are located between the different units. For example, a pound of apples can be represented as 1/2 as a fraction or as 0.5 as a decimal. However, half a kilo, 1/2 or 0.5 serves to represent exactly the same numerical value in all cases.
One of the main characteristics of decimal numbers is that they are one of the few situations in which rational numbers and non-rational numbers can be expressed on the same line. For example, if we take 1.5 as a reference, we find that 1 would be a rational number since it represents a whole part. On the other hand, the remaining 0.5 that serves to arrive at 1.5 would be a non-rational number since it is not an integer. In this way, in all the cases in which we express decimal numbers, we will find a part of each in all cases.
Let’s not forget, also, that with decimal numbers values can be expressed with total accuracy. However, in different cases we can find infinite numbers. One of the main ones is known as the number pi (it can also be expressed in the Greek alphabet). We all know it as 3.14. However, the number of values it provides is infinite, and can be represented with a multitude of decimals. The other main case where decimals are totally infinite are repeating decimals. In this case, they are those decimals in which the last unit is represented infinitely. Therefore, approximations are made or the numbers are truncated to find a value that is easier to express.
The decimal is always on the right
The measures also serve for the use of decimals. There are no exceptions or weight, length or mass or density. 1 gram is 0.001 kilos. Just like 1 kilo is 1000 grams. If we want to express small quantities as something large, the use of multiple decimals will be recommended. However, in most cases the use of few decimal places and a greater number of integer names is recommended to get options that are much more flexible when reading. Especially in those cases in which it is necessary to read and interpret multiple data that must be compared.
At a structural level, decimals are always in the same place: to the right of the comma. The first number is what is known as the integer, and after the comma, everything that comes after it is the decimals. The comma is important since it is the one that marks the separation between rational and non-rational numbers. In fact, when we carry out any type of operation with decimals, such as adding decimals, it will be necessary to take this aspect into account.
Benefits of knowing how to add decimals
All in all, there are numerous benefits of adding decimals both culturally and at the level of job opportunities. Some of the most prominent are the following:
- Do sums with more exact amounts. Data analysis is one of the top priorities for many people. Therefore, if we use more exact numbers such as decimals, we can carry out a much more precise analysis, something especially important if we have to carry out any presentation.
- Pass math. Operations with natural numbers are the first step, but if you want to continue passing mathematics, you must learn to operate correctly with decimal numbers, since it is part of the academic framework.
- Use the calculator. One of the calculator buttons is the decimal point. If we do not know the structure or the use of decimal numbers, we will not be able to apply it correctly or carry out the corresponding operations.
- Understand many measurements. On many occasions, if we do not master decimals, we cannot talk about many measurements of length, mass, or weight. Once we have a clear concept, we will understand the attribute that these numbers give us and what meaning we can give them.
How to add decimals?
Once you are clear about the concept of decimal number, it is time to understand the method to follow in order to add decimals in an appropriate and simple way. First of all it will be really useful to look back and remember when we were little and we were taught to add natural and rational numbers because the procedure is really similar. Do you remember when the teacher told you that you had to separate the units, the tenths and the hundreds? The same thing happens with decimals.
You separated the different numerical parts because each sheep must be added with its corral, so to speak. In the event that some numerical part did not have a homonym, it was said that it had an imaginary zero and, therefore, the final result was the same number that we already had. A similar procedure is followed with decimals.
As we have said before, the decimals are separated by the comma itself. Everything to the left of the comma are rational and natural numbers. Instead, everything to the right of the comma itself is considered to be the decimals. It is important when we add decimals that we join the commas before operating. The comma is the one that marks the separation between both and, therefore, both one value and another must be completely parallel.
The comma makes the difference
Everything to the left of the comma is added with its homonym and everything to the right follows the same procedure. Making a placement mistake will automatically mean that the addition will be wrong and, therefore, if you are performing an examination operation you will automatically lose points.
Once the comma is correctly placed, start the addition on the right. It performs the sum of the two values and later if the result is greater than nine, the first value is taken to the next operation. For example, six plus six equals twelve, we would put a two and the one we take it to the next number.
As we have said, if one of the two names has more units than the other, the excess is interpreted as a zero and, therefore, the same name is maintained. When we finish with the decimals, we do the same procedure with the units, adding the decimals, the hundreds and whatever is necessary in a totally staggered way. The order of the factors is one of the most important steps in adding decimals correctly. Remember also that the commutative property allows us to exchange the factors from top to bottom, since the order does not alter the product.
Use the calculator or Excel to operate with decimals
Let’s take a quick example. If we add 2.5 and 3.65 we would follow the following steps. The 5 would remain the same since since there were no 2.5 we would put the imaginary zero and it would remain. In the case of 6 we would put a one since added to 5 gives eleven and we take one and finally the 3 results in six since added to two gives five, but we took one from the previous operation. Therefore, the result would be 6.15. This is the basic structure of any addition of decimals.
However, different procedures can be used to expedite this process. The first is the calculator that uses an artificial system to perform decimal operations. Basically putting the decimal point two and five, hitting the add button and inserting 3.65 would already give us 6.15 in a few seconds. In fact, if you continue to progress in your mathematics studies, you will perform operations with much more complex decimals and, therefore, the use of the calculator is allowed.
In addition, the Excel spreadsheet, a Microsoft program, also performs operations with decimals in a simple and fast way. Just put the first number in a cell and the next value in the cell below it and look for the sum formula. The result of the operation will automatically appear in the cell below. Without a doubt, adding with decimals is a procedure that can be very simple.