# Numbers up to 100,000

## NUMBERS AND OPERATIONS A natural number 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.

#### Read and write the natural numbers up to 100,000

Throughout the 2nd grade of Elementary School you learned the three-digit numbers (from 0 to 999) and now you will discover the four and five-digit numbers.

You will know the "thousand" and the "ten thousand" as well as the rule of the use of the comma to group the figures of three in three and as a separator of the thousands.

SPANISH ENGLISH HOW TO READ A NATURAL FOUR-DIGIT NUMBER?

Any four-digit natural number is composed (taking into account the place value of its digits) by thousands (Th), hundreds (H), tens (T) and ones (O). We will always write a comma between the thousands and the hundreds digits. To correctly read and write any integer up to 9,999, initially, the digit to the left of the comma (thousands) is named, then the comma as "thousand" and, finally, the three digits to the right of the comma (hundreds, tens and ones) are read. AND HOW TO READ A NATURAL FIVE-DIGIT NUMBER?

The five-digit natural numbers are made up of ten thousands (Tth), thousands (Th), hundreds (H), tens (T) and ones (O). As with numbers with up to 4 digits, we will always write a comma between the thousands and hundreds numbers.

To properly read any whole number up to 99,999, we will first read the digits to the left of the comma (tens and ones of a thousand). Next, we will name the comma as "thousand" and, finally, we will read the digits located to the right of the point (hundreds, tens and ones).  #### Know the place value of the digits in the numbers up to 99,999: Tth - Th - H - T - O

The place value (or position) of a number is the value that any of its digits takes according to the position it occupies within the number itself (ones, tens, hundreds...).

Very important! The change of position of a digit within a number will modify the total value of the same.

SPANISH ENGLISH THE PLACE VALUE OF THE 5-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.

EQUIVALENCES BETWEEN 5-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 5 digits:  #### Compose and decompose up to 100,000 according to the value and order of position of their digits

We offer you various printable activities so that you can quickly learn to compose and decompose the natural numbers from 0 to 100,000 into ten thousands, thousands, hundreds, tens and ones.

SPANISH ENGLISH   #### Classify natural numbers up to 100,000: Greater than - Less than - Equal

We explain the concepts "greater than", "less than" and "equal to" as well as their symbols (>, <, =) with the numbers from 0 to 100,000. All this from a combination of printable cards accompanied by an educational game.

SPANISH ENGLISH   #### Identify the largest and smallest numbers in a series of natural numbers up to 100,000

We explain how to identify which is the highest number (or biggest number) and the lowest (or smallest number) with the numbers from 0 to 100,000 starting from the downloadable exercises that we have prepared.

SPANISH ENGLISH  #### Classify natural numbers up to 100,000: Before and After numbers

We provide you some PDF exercises where you have to join the natural numbers from 1 to 99,999 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 100,000

We instruct you in some activities where we randomly present you natural numbers from 0 to 100,000 on which you must recognize and interpret their position on a number line imaginary to later write its previous number (before number) and its later number (after or next number). #### Count up natural numbers up to 100,000

We have created worksheets to download and print where, from a random natural number from 0 to 100,000, you must count up until you complete an imaginary number line. #### Continue ascending series two by two, three by three... up to 100,000

We present some practical exercises where we provide you with numerical series using the numbers up to 100,000 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 100,000

We have prepared some activities ready to download and print where, from a natural number from 0 to 100,000, you must count term by term and from form descending until completing the number line. #### Continue descending series two by two, three by three... up to 100,000

We present some funny exercises where we provide you with numerical series using the numbers up to 100,000 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 100,000 by representing on a number line

We provide you with natural numbers up to 100,000 unordered so that, based on their graphic representation on a number line, you can compare them and indicate which one is its exact position or order. #### Recognize and represent natural numbers up to 100,000 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? #### Round numbers to the nearest thousand with numbers up to 100,000

Do you know how to estimate a number to thousands? And could you explain if approximating and rounding a number means the same thing? If you have doubts, we will explain it to you in detail in the following tutorial.

SPANISH ENGLISH 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.

3 , 1 8 9 is close to 3,000 because 1 < 5

5 , 4 7 0 is close to 5,000 because 4 < 5

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

4 , 9 2 5 is close to 5,000 because 9 > 5

1 , 5 6 3 is close to 2,000 because 5 = 5 #### Round numbers to the nearest ten thousand with numbers up to 100,000

Do you know how to estimate a number to ten thousands? If you have doubts, we will explain it to you in detail in the following lesson.

SPANISH ENGLISH 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.

6 2 , 9 5 7 is close to 60,000 because 2 < 5

8 4 , 0 1 8 is close to 80,000 because 4 < 5

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

1 8 , 3 0 2 is close to 20,000 because 8 > 5

4 5 , 7 2 9 is close to 50,000 porque 5 = 5 #### Recognize odd and even natural numbers up to 100,000

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. 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 3" or "Year 4":