DECIMAL NUMBERS

Maybe you are that kind of person that is thinking  that you do not need decimals at all. You are wrong, because in our daily lives of non-mathematicians we use the decimals very actively. Let us remember where we use them.

In all languages, the concept of a fraction is denoted by words with the same root as "breaking"; In Latin "decimal" is "fractura", which is derived from "frango" ("break").

Decimal fractions, in turn, were widely distributed in the late 16th century after the publication of the book "De Thiende" (Fifth) by Flemish engineer Simon Stein (1585). Cavaliers wrote about the conversion of ordinary fractions into decimals and vice versa in 1643.

The ways decimals were recorded have also been noticeably different over the centuries. Pisanski introduces the fraction bar, probably borrowing it from the Arabs. However, in the mid-17th century, mathematicians still did not use it (Mersen, 1644). The decimal point was introduced in 1529 by the Italian astronomer Maggiini, and later re-launched by Neper.

There are two types of parts of whole numbers that we used actively. These are the decimals and the fractions. What are they? I suppose many suspect that these are all those parts of the numbers that stand between the whole integers. For example, between integers 1 and 2,  which are whole numbers, some of the decimals  are: 1.0, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. 0. These examples mean a whole number and some part of another number. These parts between integers are usually separated by the comma or decimal point. Parts of whole numbers can be represented by ordinary fractions or decimals. How do you read the decimals? For example:

0.5 - read "zero and five tenths"

0.37 - read "zero thirty-seven hundredths"

0.000009 - we read "zero and nine millions".

2.05 - read "two and five hundredths";

41,057 - read "forty-one fifty-seven thousandths"

I think there is no one who does not use decimal fractions in almost every day of his life. I believe everyone needs to use non whole numbers in certain situations. Almost everyone uses "halves", "quarters", "thirds". Perhaps not everyone has to write it with numbers and hardly anyone is so diligent and precise to use the numbers after the comma with great precision, using exact numbers.

In which cases of everyday life can we use decimals? In all cases, when we talk about money, for example. If we have to mention pennies, we use "0.50" for example and so on. When we measure height or distance, we also use decimals to indicate that the measure is not just in whole numbers. For example: the height of the table is 1, 56 cm, it is high 1, 62 cm and the like. In all cases, when we are using cooking recipes, the product weights could be written with decimals if it is not for whole kilograms, but even between kilograms the markings are with decimals. Every time we determine the temperature we use decimals.

What mathematical operations are possible to do with decimal fractions? Practically, we can collect, subtract, multiply, and divide decimals to one another, and to whole numbers. I suppose that is where most of us will have difficulties, but in our daily lives to do these operations we can arrange the decimals in a column to make the calculations easy to happen or a calculator can always help. 

Rules for comparing decimals:

• From two decimals the biggest is the one that has the biggest first/main number.

• If the whole parts are equal, we compare the number of their tenths. Greater is this decimal, which has a larger number of tenths.

• If the numbers of the tenths are equal, we compare the number of the hundreds, etc.

If the numbers before the decimal point and decimal parts are equal, then the decimals are equal.

Example: Which of the decimals is the greatest: 3 and 1.24.

From the fact that for the whole parts of the decimals is fulfilled 3 > 1, it is true that 3 > 1.24

To add two decimals this means, we add - units of units, ten-tenths, hundreds with hundredths, thousands with thousandths. If in some decimals there is no figure given, we can write zero.

Basic rules for adding decimals:

• We equalize the number of digits of the two decimals.

• Write the numbers one by one so that the decimal points are one below the other

• We add the numbers as we add the whole numbers.

• We place the decimal point.

  For example: 0.356 + 43.7 = 44.056

We subtract decimals in a similar way.

To multiply two decimals, we follow the following rules:

• Sort the numbers one by one;

• We ignore the comma and multiply the numbers as we multiply the whole numbers

• As a result, we move the decimal point, as many digits from right to left as the fraction of the decimal fractions

 

Example: 12,25⋅10 = 122,50

Example: 2,327,100 = 232,700

Example: 1,3678,1000 = 1367,8000

I guess you agree that decimals are not easy to work with because you have to remember many details if you want to be accurate. It is all about place value.  In addition, if you have to multiply them or divide one by another quickly, it is hard   to be done mentally. That is why we round the decimal numbers to the nearest whole numbers, because with a whole number it is easier to work and they are easy to remember. For example, 0, 6 is rounded to 1, and 1, 2 is rounded to 1. Here we follow the known rule, taking into account the second number - whether it is greater or lesser than five. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. 1. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 33 rounded to the nearest ten is 30.

It is  not exaggerated to say that whenever we work with money and measures, we round the decimals. 

Are any decimal numbers in nature and in our human life? Nature is all about wholeness. If the idea of a part of something is presented in nature, it is mainly in a way how the humans are seeing the life around us. In our life we very often use the expression ‘part of me’ with a meaning that we are coming to a point when our wholeness cannot happen, at least about certain things. Usually it is a moment of disbalance and lack of harmony inside. Part of me understands this but part of me doesn’t. How can we measure this decimal of our brain and mind? What part of the whole is that? It is hard to say. Or let’s take a different expression: I left part of my heart there. Can we measure this part with a decimal number? Maths is powerless in many cases, especially when the human language shows its creative expressive power and abilities. From a spiritual point of view we have to aim to achieve and to maintain wholeness for our mind, body and heart. All these three dimensions need to be at the same time in the same place. So there is peace, calmness and love for every single part of our whole being.

Here are some activities for you: Activity 1: Can you make a  list of all the cases when you have had to use decimals today? Specify which maths operations you performed with them. Activity 2: Can you write down all decimal numbers that lie between number 0 and 10? Don’t forget about the place value.