A ** natural number (ℕ)** is considered any of the numbers used to ** count the elements ** of a set or **sort**.

__ Our System of Numeration (or Numeral System) is both decimal and positional: __

- ** Decimal**, also called ** base ten numerals**, because ten units of a ** lower order ** form a unit of the ** immediately higher order ** (10 ones equals 1 ten, 10 tens equals 1 hundred...).

- ** Positional**, because the value of a figure will depend on the ** place it occupies ** within the number (ones, tens, hundreds...).

Furthermore, the set of natural numbers ** is represented by ℕ ** and is distributed as follows: ** ℕ = { 1, 2, 3, 4, 5, 6, 7, 8 , 9, ... } ** and, therefore, it is considered that the natural numbers, as a whole, are ** ordered**, ** positive ** and tend to ** infinity**.

DO YOU KNOW THE ORIGIN OF THE CURRENT NUMBERS?

We call the numbers with which we learn every day "**Arabic numerals**", which represent the ** symbols ** or ** glyphs ** that we use when we write the 1, the 2, the 3, the 4, the 5...

They are so named because it was the ** Arabs ** who introduced the numbers in **Europe**, but who really invented them were the mathematicians of ** India ** and ** China ** between the 5th and 8th centuries.

The first representation of Arabic numerals in Occident belongs to an anonymous manuscript called "**Chronicon Albeldense**" (also known as "*Codex Conciliorum Albeldensis seu Vigilanus*"), which was written in Latin and published in 883 A.D.

Next, we present __ how Arabic numerals were originally written__ and how they __ evolved to become the current numbers__:

THE NATURAL NUMBERS REGARDING THE NUMERICAL SET

We provide you with a ** visual scheme ** so that you can correctly locate the __ natural numbers__ (ℕ) within the set (also called "mathematical notation") of the integers (ℤ), rational (ℚ), real (ℝ) and complex (ℂ):

Remember, ** mathematical symbols ** convey a ** formal language based on universal rules ** and represent in themselves a __ concept__, a __ relationship__, an __ operation__ or a __ mathematical formula__ and, therefore, should never be understood as a simple abbreviation.

#### Read and write the natural numbers up to 10,000,000

Throughout the ** 3rd year of Primary Education ** you learned to read and write ** four and five digit numbers (up to 99,999) ** and now you will discover the ** six and seven-digit numbers**.

You will know the "**millions**" and the "**hundred thousands**" as well as the ** rule of the use of the comma ** to group the digits of three in three and as a separator from the thousands and the millions.

HOW TO READ A NATURAL SIX-DIGIT NUMBER?

Any ** six-digit natural number ** will be made up of ** hundreds of thousands ** (H th), ** tens of thousands ** (T th), ** ones of thousands ** (Th), ** hundreds ** (H), ** tens ** (T) and ** ones ** (O). We will always write a ** comma ** between the ** one thousands** and ** hundreds ** numbers.

SPANISH

ENGLISH

__ To correctly read any whole number up to 999,999__ we will first read the ** figures to the left of the comma ** (hundred thousands, ten thousands and one thousands); then we will name the ** comma as "thousand" ** and, finally, we will read the ** figures located to the right of the point ** (hundreds, tens and ones).

AND HOW TO READ A NATURAL SEVEN-DIGIT NUMBER?

__ In the whole numbers of seven digits, we will write a separator comma in the following cases: __

- Between the digit of ** millions** (M) and ** hundred thousands ** (H th) to identify "**millions**".

- Between the digit of **thousands** (Th) and ** hundreds ** (H) to identify the "**thousands**".

__ To correctly read any whole number up to 9,999,999__ first the **digit on the left ** is read, then the ** comma is read as "million" (singular) or "millions" (plural)**; then the ** three digits located between the two commas ** are named as if they were a three-digit number with ones, tens and hundreds. Next, the ** comma is read as "thousand" ** and finally the three ** digits to the right of the comma ** are read.

#### Know the place value of figures with numbers up to 10,000,000

PLACE VALUE OF THE 6 AND 7 DIGIT NUMBERS

- The "__one__" ** ** is the ** smallest integer element ** that we can use to count and represents the ** last digit ** of any whole number.

- The "** ten**" represents

**groupings of ones of 10 in 10**and corresponds to the

**penultimate digit**of any whole number.

- The "** hundred**" groups the

**tens of 10 into 10**as well as the

**ones of 100 into 100**; and occupies the

**third to last digit**of any whole number.

- The "** thousand**" brings together the

**hundreds of 10 in 10**, the

**tens of 100 in 100**and the

**ones of 1,000 in 1,000**being located in the

**fourth digit**of the whole numbers.

- The "** ten thousand**" group the

**thousands in groups of 10**, the

**hundreds in groups of 100**, the

**tens in groups of 1,000**and the

**ones in groups of 10,000**being the equivalent of the

**fifth digit**according to its place value.

- The "** hundred thousand**" encompasses the

**ten thousands of 10 in 10**, the

**one thousand in groups of 100**, the

**hundreds in groups of 1,000**, the

**tens in groups of 10,000**and the

**ones in groups of 100,000**being located in the

**sixth digit**of the whole numbers.

- The "** million**" comprises the

**ones of 1,000,000 in 1,000,000**, the

**tens of 100,000 in 100,000**, the

**hundreds of 10,000 in 10,000**, the

**thousands of 1,000 in 1,000**, the

**ten thousands of 100 in 100**and the

**hundred thousands of 10 in 10**. Represents the

**seventh digit**of any natural number.

EQUIVALENCES BETWEEN 7-DIGIT NUMBERS

We present a ** comparative table ** so that you can visually understand the ** equivalences ** existing between the ** digits ** of the __ natural numbers of up to 7 digits__:

#### Compose and decompose up to 10,000,000 according to the value and order of position of their digits

#### Classify natural numbers up to 10,000,000: Greater than - Less than - Equal

#### Identify the largest and smallest numbers in a series of natural numbers up to 10,000,000

#### Classify natural numbers up to 10,000,000: Before and After numbers

We provide you some ** PDF exercises ** where you have to join the ** natural numbers from 1 to 9,999,999 ** of the central column with their ** previous number ** (left) and their **following number** (right):

- The ** before number ** (or previous number) is the one that has ** one less unit ** than the number from which we started and, therefore, we will ** jump to the left ** in the ** number line**.

- The ** after number ** (or next number) will be the one that has ** one more unit ** than the number we started from and, therefore, we will ** jump to the right ** in the ** number line**.

#### Write the numbers before and after a given with natural numbers up to 10,000,000

#### Count up natural numbers up to 10,000,000

#### Continue ascending series two by two, three by three... up to 10,000,000

We present some ** practical exercises ** where we provide you with ** numerical series using the numbers up to 10,000,000 ** in which, to solve them satisfactorily, you must ** count in ascending order ** giving ** numeric jumps ** two by two (2's), three by three (3's), four by four (4's)...

#### Count down natural numbers up to 10,000,000

#### Continue descending series two by two, three by three... up to 10,000,000

We present some ** funny exercises ** where we provide you with ** numerical series using the numbers up to 10,000,000 ** in which, to solve them correctly, you must ** count in descending order ** giving ** numeric jumps ** two by two (2's), three by three (3's), four by four (4's)...

#### Order numbers up to 10,000,000 by representing on a number line

#### Recognize and represent natural numbers up to 10,000,000 on abacus

Do you know what an ** abacus ** is? And could you explain ** what it is for**? We explain it to you:

An ** abacus ** is an ancient ** calculation tool ** used to solve ** arithmetic operations ** such as addition and subtraction. In addition, today it is very useful to promote ** learning ** of ** numerical decomposition ** and the ** place value ** of any number.

Do you dare to solve the ** activities ** that we propose using the ** abacus**?

#### Approximate numbers to the one, ten and / or hundred thousand and / or the nearest million

ROUNDING TO THE NEAREST THOUSAND

__For rounding off to the nearest 1,000 we will always look at the digit in the hundreds place:__

- If the ** digit of the hundreds is 0, 1, 2, 3 or 4 ** (less than 5), we will approximate the ** thousand given**, that is, thousand will remain as it appears.

- If the ** hundred digit is 5, 6, 7, 8 or 9 ** (greater than or equal to 5), we will approximate the ** immediately higher thousand. **

SPANISH

ENGLISH

**3 , 1 8 9** is close to

**3,000**because

__1__< 5**4 , 9 2 5** is close to

**5,000**because

__9__> 5ROUNDING TO THE NEAREST TEN THOUSAND

__For rounding off to the nearest 10,000 we will always look at the digit in the thousands place:__

- If the ** digit of the thousands is 0, 1, 2, 3 or 4 ** (less than 5), we will approximate the ** ten thousand given**, that is, ten thousand will remain as it appears.

- If the ** thousand digit is 5, 6, 7, 8 or 9 ** (greater than or equal to 5), we will approximate the ** immediately higher ten thousand. **

SPANISH

ENGLISH

**6 2 , 9 5 7** is close to

**60,000**because

**2 < 5**

**1 8 , 3 0 2** is close to

**20,000**because

**8 > 5**

ROUNDING TO THE NEAREST HUNDRED THOUSAND

__For rounding off to the nearest 100,000 we will always look at the digit in the ten thousands place:__

- If the ** digit of the ten thousands is 0, 1, 2, 3 or 4 ** (less than 5), we will approximate the ** hundred thousand given**, that is, hundred thousand will remain as it appears.

- If the ** ten thousand digit is 5, 6, 7, 8 or 9 ** (greater than or equal to 5), we will approximate the ** immediately higher hundred thousand. **

SPANISH

ENGLISH

**6 3 5 , 0 8 9** is close to

**600,000**because

__3__< 5**8 5 2 , 9 9 5** is close to

**900,000**because

__5__= 5ROUNDING TO THE NEAREST MILLION

__For rounding off to the nearest 1,000,000 we will always look at the digit in the hundred thousands place:__

- If the ** digit of the hundred thousands is 0, 1, 2, 3 or 4 ** (less than 5), we will approximate the ** million given**, that is, million will remain as it appears.

**2 , 4 0 8 , 5 7 6** is close to

**2,000,000**because

__4__< 5- If the ** hundred thousand digit is 5, 6, 7, 8 or 9 ** (greater than or equal to 5), we will approximate the ** immediately higher million. **

**7 , 6 9 5 , 3 1 4** is close to

**8,000,000**because

__6__> 5#### Recognize odd and even natural numbers up to 10,000,000

Do you know what ** even numbers ** and ** odd numbers** are? And could you explain ** how the even numbers differ from the odd numbers?**

**The even natural numbers are those that end in 0, 2, 4, 6 and 8 while the odd natural numbers are those that end in 1, 3, 5, 7 and 9.**

**Concentrate on your work and try hard** and you will see **how you will become a great mathematician**.

**Do you want access to more Fourth Grade learning?**

**Select more exercises, worksheets and activities of Mathematics for each of the 4 learning blocks of the Educational Curriculum ("Numbers and Operations", "Quantities and Measurements", "Geometric and Spatial Reasoning" and "Data Analysis and Probability") aimed at improving the logical-mathematical competencies and skills that are developed throughout "Grade 4" or "Year 5":**

**NUMBERS AND OPERATIONS**

**FOURTH GRADE**

**QUANTITIES AND MEASUREMENTS**

**FOURTH GRADE**

**GEOMETRIC AND SPATIAL REASONING**

**FOURTH GRADE**

**DATA ANALYSIS AND PROBABILITY**

**FOURTH GRADE**

**Boys and girls should be taught to think, not what to think**

**Margaret Mead**