What are natural numbers

The study of mathematics begins with natural numbers and operations with them. But intuitively we already know a lot from an early age. In this article, we will get acquainted with the theory and learn how to write and pronounce complex numbers correctly.

In this publication, we will consider the definition of natural numbers, list their main properties and mathematical operations performed with them. We also give a table with natural numbers from 1 to 100.

Definition of natural numbers

Integers – these are all the numbers that we use when counting, to indicate the serial number of something, etc.

natural series is the sequence of all natural numbers arranged in ascending order. That is, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.

The set of all natural numbers denoted as follows:

N={1,2,3,…n,…}

N is a set; it is infinite, because for anyone n there is a larger number.

Natural numbers  are numbers that we use to count something specific, tangible.

Here are the numbers that are called natural: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, etc.

A natural series is a sequence of all natural numbers arranged in ascending order. The first hundred can be seen in the table.

Simple Properties of natural numbers

  1. Zero, non-integer (fractional) and negative numbers are not natural numbers. For example:-5, -20.3, 3/7, 0, 4.7, 182/3 and more
  2. The smallest natural number is one (according to the property above).
  3. Since the natural series is infinite, there is no largest number.

Table of natural numbers from 1 to 100

12345678910
11121314151617181920
21222324252627282930
31323334353637383940
41424344454647484950
51525354555657585960
61626364656667686970
71727374757677787980
81828384858687888990
919293949596979899100

What operations are possible on natural numbers

  • addition:
    term + term = sum;
  • multiplication:
    multiplier × multiplier = product;
  • subtraction:
    minuend − subtrahend = difference.

In this case, the minuend must be greater than the subtrahend, otherwise the result will be a negative number or zero;

  • division:
    dividend: divisor = quotient;
  • division with remainder:
    dividend / divisor = quotient (remainder);
  • exponentiation:
    a b , where a is the base of the degree, b is the exponent.
What are Natural Numbers?

Decimal notation of a natural number

At school, we go through the topic of natural numbers in the 5th grade, but in fact, a lot of things can be intuitively clear to us even earlier. Let’s talk about important rules.
We regularly use numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. When writing any natural number, you can use only these numbers without any other symbols. We write the numbers one by one in a line from left to right, using the same height.
Examples of correct writing of natural numbers: 208, 567, 24, 1467, 899112. These examples show us that the sequence of numbers can be different and some can even be repeated.
077, 0, 004, 0931 are examples of incorrect notation of natural numbers, because zero is on the left. The number cannot start from zero. This is the decimal representation of a natural number.

Quantitative meaning of natural numbers

Natural numbers carry a quantitative meaning, that is, they act as a tool for numbering.
Imagine that we have a banana 🍌 in front of us. We can record that we see 1 banana. In this case, the natural number 1 is read as “one” or “one”.
But the term “unit” has another meaning: that which can be considered as a whole. An element of a set can be denoted by a unit. For example, any tree from a set of trees is a unit, any leaf from a set of leaves is a unit.
Imagine that we have 2 bananas 🍌🍌 in front of us. The natural number 2 is read as “two”. Further, by analogy:
🍌🍌🍌 3 items (“three”)
🍌🍌🍌🍌 4 items (“four”)
🍌🍌🍌🍌🍌 5 items (“five”)
🍌🍌🍌🍌🍌🍌 6 items (“six”)
🍌🍌🍌🍌🍌🍌🍌 7 items (“seven”)
🍌🍌🍌🍌🍌🍌🍌🍌 8 items (“eight”)
🍌🍌🍌🍌🍌🍌🍌🍌🍌 9 items (“nine”)
The main function of a natural number is to indicate the number of items.
If the record of a number matches the number 0, then it is called “zero”. Recall that zero is not a natural number, but it can mean an absence. Zero items means none.

One-digit, two-digit and three-digit natural numbers

A single-digit natural number  is a number that has one sign and one digit. Nine single-digit natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9.
Two-digit natural numbers  are those that have two signs and two digits. The numbers may be repeated or different. For example: 88, 53, 70.
If the set of objects consists of nine and one more, then we are talking about 1 ten (“one dozen”) of objects. If one ten and one more, then we have 2 tens (“two tens”) and so on.
In essence, a two-digit number is a set of single-digit numbers, where one is written on the right and the other on the left. The number on the left shows the number of tens in the natural number, and the number on the right shows the number of units. There are 90 two-digit natural numbers in total.
Three-digit natural numbers  are numbers with three digits and three digits. For example: 666, 389, 702.
One hundred is a set of ten tens. One hundred and another hundred – 2 hundreds. Let’s add another hundred – 3 hundreds.
This is how a three-digit number is written: natural numbers are written one after the other from left to right.
The rightmost single digit indicates the number of units, the next one indicates the number of tens, and the leftmost one indicates the number of hundreds. The number 0 indicates the absence of units or tens. So 506 is 5 hundreds, 0 tens and 6 ones.
Four-digit, five-digit, six-digit and other natural numbers are defined in the same way.

Multivalued natural numbers

Multi-digit natural numbers consist of two or more digits.
1,000 is a set with ten hundred, 1,000,000 is a thousand thousand, and one billion is a thousand million. A thousand million, just imagine! That is, we can consider any multi-valued natural number as a set of single-valued natural numbers.
For example, 2 873 206 contains: 6 units, 0 tens, 2 hundreds, 3 thousand, 7 tens of thousands, 8 hundreds of thousands and 2 million.
How many natural numbers are there?
One-digit 9, two-digit 90, three-digit 900, etc.

Properties of natural numbers

We already know about the features of natural numbers. And now let’s talk about their properties in detail:
Definition of a natural number
Natural numbers  are numbers that we use to count something specific, tangible.
Here are the numbers that are called natural: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, etc.
A natural series is a sequence of all natural numbers arranged in ascending order. The first hundred can be seen in the table.

Features of natural numbers

The smallest natural number: one (1).
Largest natural number: does not exist. The natural series is infinite.
In the natural series, each next number is greater than the previous one by one: 1, 2, 3, 4, 5, 6, 7, etc.
The set of all natural numbers is usually denoted by the Latin letter N.
What operations are possible on natural numbers
addition:
term + term = sum;
multiplication:
multiplier × multiplier = product;
subtraction:
minuend − subtrahend = difference.
In this case, the minuend must be greater than the subtrahend, otherwise the result will be a negative number or zero;
division:
dividend: divisor = quotient;
division with remainder:
dividend / divisor = quotient (remainder);
exponentiation:
a b , where a is the base of the degree, b is the exponent.
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Properties of natural numbers

We already know about the features of natural numbers. And now let’s talk about their properties in detail:
  • set of natural numbers infinite and starts from one (1)
  • each natural number is followed by another it is more than the previous one by 1
  • the result of dividing a natural number by one (1) natural number itself: 5 : 1 = 5
  • the result of dividing a natural number by itself unit (1): 6 : 6 = 1
  • commutative law of addition from the rearrangement of the places of the terms, the sum does not change: 4 + 3 = 3 + 4
  • associative law of addition the result of adding several terms does not depend on the order of operations: (2 + 3) + 4 = 2 + (3 + 4)
  • commutative law of multiplication from the permutation of the places of the factors, the product will not change: 4 × 5 = 5 × 4
  • associative law of multiplication the result of the product of factors does not depend on the order of operations; you can at least like this, at least like that: (6 × 7) × 8 = 6 × (7 × 8)
  • distributive law of multiplication with respect to addition to multiply the sum by a number, you need to multiply each term by this number and add the results: 4 × (5 + 6) = 4 × 5 + 4 × 6
  • distributive law of multiplication with respect to subtraction to multiply the difference by a number, you can multiply by this number separately reduced and subtracted, and then subtract the second from the first product: 3 × (4 − 5) = 3 × 4 − 3 × 5
  • distributive law of division with respect to addition to divide the sum by a number, you can divide each term by this number and add the results: (9 + 8) : 3 = 9 : 3 + 8 : 3
  • distributive law of division with respect to subtraction to divide the difference by a number, you can divide by this number first reduced, and then subtracted, and subtract the second from the first product: (5 − 3) : 2 = 5 : 2 − 3 : 2

Natural number digits and the value of the digit

Recall that the position on which the digit stands in the record of the number depends on its value. So, for example, 1123 contains: 3 units, 2 tens, 1 hundred, 1 thousand. At the same time, we can formulate it differently and say that in a given number 1123, the number 3 is located in the units digit, 2 in the tens digit, 1 in the hundreds digit, and 1 serves as the value of the thousands digit.
The digit  is the position, the location of the digit in the notation of a natural number.
Each category has its own name. The most significant digits are always on the left, and the least significant digits are always on the right. To remember faster, you can use a table.
The number of digits always corresponds to the number of characters in the number. This table has the names of all the digits for a number that consists of 15 characters. The following digits also have names, but they are rarely used.
The lowest (least significant) digit of a multivalued natural number is the units digit.
The highest (highest) digit of a multi-valued natural number is the digit corresponding to the leftmost digit in a given number.
You have probably noticed that textbooks often put small spaces when writing multi-digit numbers. This is done so that natural numbers are easy to read. And also – to visually separate different classes of numbers.
A class  is a group of digits that contains three digits: units, tens and hundreds.

Decimal number system

People at different times used different methods of writing numbers. And each number system has its own rules and features.
The decimal number system  is the most common number system in which ten digits are used to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
In the decimal system, the value of the same digit depends on its position in the notation of the number. For example, the number 555 consists of three identical digits. In this number, the first digit from the left means five hundred, the second – five tens, and the third – five units. Since the value of a digit depends on its position, the decimal number system is called positional.

Question for self-test

How many natural numbers can be marked on the coordinate ray between points with coordinates:
0 and 15;
20 and 50;
100 and 130?
Источник – Онлайн школа Skysmart: https://skysmart.ru/articles/mathematic/naturalnye-chisla

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