People started using numbers a long time ago. To do this, they mainly used their fingers. People simply pointed on their fingers the number of objects they wanted to report. This is how the names of the numbers arose and gradually became fixed: 1, 2, 3, 4, 5, 6, 7, 8, 9. But what if there are more objects than fingers? Then we had to show our hands several times, which, of course, did not suit everyone. And then smart people, either in India or in the Arab world, came up with another number - zero, which means the absence of objects, and with it the decimal number system. Decimal because ten digits are used: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 .

Number and decimal number system

Numbers differ from numbers in that may consist of one or several digits written in a row. The decimal number system is a positional system. The meaning of a number depends on the place (position) it occupies in the number. Digits are also numbers, but they consist of one digit, which occupies a position in the ones place. If you need to write down a number that is next in order to 9, then you need to move to the next digit - the tens digit.

Thus, the next number will be 10 - one ten, zero units, 11 - one ten one unit, 12 - one ten two units, 25 - two tens five units and so on. After the number 99 comes the number 100 - one hundred zero tens zero ones. Then the digits of thousands, tens of thousands, hundreds of thousands, millions, etc. are added. Thus, by adding new digits on the left, we can use larger and larger numbers.

From counting objects, which is carried out using natural numbers, humanity naturally moved on to counting measures of length, weight and time. And then the problem arose of how to count non-integer parts. appeared naturally common fractions: half, third, quarter, fifth, etc. They began to be written down in the form of a numerator and a denominator: in the denominator they wrote down how many parts the whole is divided into, and in the numerator - how many such parts are taken. For example, half is 1/2, a third is 1/3, a quarter is 1/4, etc.

Decimals

As humanity increasingly used the decimal number system, to give records fractional numbers to decimal form, fractions with denominators in the form of digit units 10, 100, 1000, 10,000, etc. began to be written in the form decimals, Where fraction separated from the whole by a comma or period. For example, 1/10 = 0.1, 1/100 = 0.01, 1/1000 = 0.001, 1/10000 = 0.0001. Moreover, ordinary fractions began to be converted into decimal form by dividing the numerator by the denominator, and if exact replacement was not possible, then it was carried out approximately, with an accuracy that satisfied the practical needs of people.

One should not think that the decimal number system, with ten digits, which is familiar to us, has always been used everywhere. For example, in the famous Roman Empire, completely different numbers were used, which are still sometimes used to number chapters in books, designate centuries, etc. We call these Roman numerals and there were only seven of them: I - one, V - five, X - ten, L - fifty, C - one hundred, D - five hundred, M - one thousand. All other numbers were written using these seven digits. If a smaller number came before a larger one, then it was subtracted from the larger one, and if after a larger one, then it was added to it. Some identical numbers can be repeated no more than three times in a row. For example, II – two, III – three, IV – four (5 – 1 = 4), VI – six (5 + 1 = 6).

Other number systems

With the beginning of the development of computer technology, other number systems began to be used, closer to machines than to people. For example, a natural number system for computers is the binary number system, consisting of two digits: 0 and 1. For example, let’s write several numbers in a row using the binary number system: 0 – zero, 1 – one, 10 – two (zero ones and one two), 11 – three (one one and one two), 100 – four (zero ones, zero twos, one four), 101 – five (one one, zero twos, one four), etc. That is, the digit units here differ by a factor of two: twos, fours, eights, etc.

In addition to the binary number system, octal and hexadecimal systems are now widely used in computing and programming.

All people from early childhood are familiar with the numbers with which they count objects. There are only ten of them: from 0 to 9. That is why the number system is called decimal. Using them you can write down absolutely any number.

For thousands of years, people have used their fingers to mark numbers. Today, the decimal system is used everywhere: to measure time, when selling and buying something, in various calculations. Each person has his own numbers, for example, in his passport, on a credit card.

By milestones of history

People are so accustomed to numbers that they don’t even think about their importance in life. Probably many have heard that the numbers that are used are called Arabic. Some were taught this at school, while others learned it by accident. So why are the numbers called Arabic? What is their story?

And it is very confusing. There are no reliably accurate facts about their origin. It is known for sure that it is worth thanking the ancient astronomers. Because of them and their calculations, people today have numbers. Astronomers from India, somewhere between the 2nd and 6th centuries, became acquainted with the knowledge of their Greek colleagues. From there the sexagesimal and round zero were taken. Greek was then combined with the Chinese decimal system. The Hindus began to denote numbers with one sign, and their method quickly spread throughout Europe.

Why are numbers called Arabic?

From the eighth to the thirteenth centuries, Eastern civilization actively developed. This was especially noticeable in the field of science. Great attention was paid to mathematics and astronomy. That is, accuracy was held in high esteem. Throughout the Middle East, the city of Baghdad was considered the main center of science and culture. And all because it was geographically very advantageous. The Arabs did not hesitate to take advantage of this and actively adopted many useful things from Asia and Europe. Baghdad often gathered prominent scientists from these continents, who passed on experience and knowledge to each other and talked about their discoveries. At the same time, the Indians and Chinese used their own number systems, which consisted of only ten characters.

It wasn't invented by the Arabs. They simply highly appreciated their advantages compared to the Roman and Greek systems, which were considered the most advanced in the world at that time. But it is much more convenient to display indefinitely with only ten characters. The main advantage of Arabic numerals is not the ease of writing, but the system itself, since it is positional. That is, the position of the digit affects the value of the number. This is how people define units, tens, hundreds, thousands, and so on. It is not surprising that Europeans also took this into account and adopted Arabic numerals. What wise scientists there were in the East! Today this seems very surprising.

Writing

What do Arabic numerals look like? Previously, they were composed of broken lines, where the number of angles was compared with the size of the sign. Most likely, Arab mathematicians expressed the idea that it was possible to associate the number of angles with the numerical value of a digit. If you look at the ancient spelling, you can see how big the Arabic numerals are. What kind of abilities did scientists have in such ancient times?

So, zero has no angles when written. The unit includes only one acute angle. The deuce contains a pair of acute angles. A three has three corners. Its correct Arabic spelling is obtained by drawing the postal code on envelopes. The quad includes four corners, the last of which creates the tail. The five has five right angles, and the six, respectively, has six. With the correct old spelling, seven has seven corners. Eight - out of eight. And nine, it’s not hard to guess, is out of nine. That is why the numbers are called Arabic: they invented the original style.

Hypotheses

Today there is no clear opinion about the formation of the writing of Arabic numerals. No scientist knows why certain numbers look the way they do and not some other way. What were ancient scientists guided by when giving numbers shapes? One of the most plausible hypotheses is the one with the number of angles.

Of course, over time, all the angles of the numbers were smoothed out, they gradually acquired the familiar modern man appearance And for a huge number of years, Arabic numerals around the world have been used to denote numbers. It's amazing that just ten characters can convey unimaginably large meanings.

Results

Another answer to the question of why numbers are called Arabic is the fact that the word “number” itself is also of Arabic origin. Mathematicians translated the Hindu word “sunya” into their native language and it turned out “sifr”, which is already similar to what is pronounced today.

This is all that is known about why the numbers are called Arabic. Perhaps modern scientists will still make some discoveries in this regard and shed light on their occurrence. In the meantime, people are content with only this information.

In the names of Arabic numbers, each digit belongs to its own category, and every three digits form a class. Thus, the last digit in a number indicates the number of units in it and is called, accordingly, the ones place. The next, second from the end, digit indicates the tens (tens place), and the third from the end digit indicates the number of hundreds in the number - the hundreds place. Further, the digits are also repeated in turn in each class, denoting units, tens and hundreds in the classes of thousands, millions, and so on. If the number is small and does not have a tens or hundreds digit, it is customary to take them as zero. Classes group digits in numbers of three, often placing a period or space between classes in computing devices or records to visually separate them. This is done to make it easier to read. large numbers. Each class has its own name: the first three digits are the class of units, followed by the class of thousands, then millions, billions (or billions), and so on.

Since we use the decimal system, the basic unit of quantity is ten, or 10 1. Accordingly, as the number of digits in a number increases, the number of tens also increases: 10 2, 10 3, 10 4, etc. Knowing the number of tens, you can easily determine the class and rank of the number, for example, 10 16 is tens of quadrillions, and 3 × 10 16 is three tens of quadrillions. The decomposition of numbers into decimal components occurs in the following way - each digit is displayed in a separate term, multiplied by the required coefficient 10 n, where n is the position of the digit from left to right.
For example: 253 981=2×10 6 +5×10 5 +3×10 4 +9×10 3 +8×10 2 +1×10 1

The power of 10 is also used in writing decimal fractions: 10 (-1) is 0.1 or one tenth. In a similar way to the previous paragraph, you can also expand a decimal number, n in this case will indicate the position of the digit from the decimal point from right to left, for example: 0.347629= 3×10 (-1) +4×10 (-2) +7×10 (-3) +6×10 (-4) +2×10 (-5) +9×10 (-6 )

Names of decimal numbers. Decimal numbers are read by the last digit after the decimal point, for example 0.325 - three hundred twenty-five thousandths, where the thousandth is the place of the last digit 5.

Table of names of large numbers, digits and classes

The term “number” arose in ancient times, when people first managed to count objects. At first, counting was done on fingers. Then they began to count by the notches on the sticks. Over time, people began to understand numbers free of objects and persons that could be counted. That's why the Slavs came up with the word "number".

In the 15th century, special signs began to spread in European countries, with the help of which numbers were designated (numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0). It was an invention of the Indians, and later they appeared in Europe thanks to the Arabs (Arabic numerals). Why are they the way they are?

If you look closely at these Arabic numbers, you will notice that each number corresponds to the number of angles that can be found on that number. The number 0 has no angles, the number 1 has one angle, and the number 9 has all nine angles.

Since the middle of the 18th century, the word number acquired a new meaning - number sign.

What is the difference between a number and a number?

So, the word has a number and a digit different meaning and origin. Number is a unit of counting that expresses quantity (one house, two houses, etc.). A number is a sign (symbol) that indicates the value of a number. To write numbers, Arabic numerals are used - 1, 2, 3... 9, and sometimes Roman numerals - I, II, III, IV, V, etc.

In conversation, the words number and figure replace each other. For example, by number we understand not only the quantity, but also the sign that expresses it.

Names and sequence of natural numbers from 1 to 20

The numbers 1,2,3,4,5,6,7,8,9,0, which are used in counting, are natural numbers. Using the numbers 0,1,2,3,4,5,6,7,8,9 you can write natural number. This notation of numbers is called decimal. Each class has three categories.

• Below is a table of categories.

Classes Billions Millions Thousands Units

Place Hundreds Tens Units Hundreds Tens Units Hundreds Tens Units Hundreds Tens Units

1st number 2 0 0 3 2 4 0 6 0 0 8 1

2nd number 4 7 0 0 0 0 2 0 2 3 0 0

3rd number 5 0 0 1 0 0 0 3 1 0 9 0

This is how some numbers are read:

• 1) ten billion thirty-two million four hundred sixty-nine thousand eight;
• 2) four hundred seventy billion one hundred thirty thousand three hundred;
• 3) five billion three million three hundred ten.

There are also such classes: the class of trillions, the class of quadrillions, the class of quintillions.

Comparison of natural numbers

To compare two natural numbers means to establish which one is greater (less) than the other. The result of a comparison is written as an inequality using the signs > (greater than) and< (меньше).

• 53607 < 400032
• 96091 < 96100

Literal expressions

Task

Mom bought a pen for 5 rubles. and several notebooks at a price of 2 rubles per 1 notebook. How many rubles did mom pay for the purchase if she bought 3 notebooks, 6 notebooks, 10 notebooks, n notebooks? Write an expression to solve the problem.

1) 3 notebooks: 2 x 3 + 5;

2) 6 notebooks: 2 x 6 + 5;

3) 10 notebooks: 2 x 10 + 5;

4) n notebooks: 2 x n + 5.

Expressions 1,2,3 are called numerical expressions, and expression 4, in addition to numbers connected by action signs, includes the letter n.

It is impossible to imagine life without counting. In everyday life, each of us encounters numbers and numbers every day, without even thinking about where we work with numbers and where we work with numbers, and what is their difference.

The definition of a numeral is as follows: a sign adopted and used to denote a quantity (expressed in numerical equivalent). And a number is an expression of quantitative characteristics in convenient form, through numbers. From here there are two conclusions: numbers consist of digits and a digit has sign properties (conditionality, recognition, immutability, etc.). Numbers also have symbolic properties, since they are a kind of abstraction, but they only have them because they consist of numbers. But we not only use a number as a component of a number, but also as an independent analogue of a number when we are talking about objects in quantities from one to nine inclusive (since the numbers 10 are from zero to nine). These features apply not only to Arabic numerals, but also to Roman ones. Similarly, I V X L C D M are Roman numerals, but V I I I is a Roman numeral, although conceptually in another number system it corresponds to the Arabic numeral 8.

Conclusions website

1. The numbers are units of counting from 0 to 9, the rest are numbers.
2. Numbers are made up of digits.
3. Numbers are signs, and numbers are a quantitative abstraction.
4. The numbers and numbers of different number systems do not coincide so much that a number in one system may turn out to be a number in another, and all because these are abstract concepts invented by man.