Decimal numbers: 6th grade math course in PDF.

A sixth grade math lesson on decimal numbers, in this lesson that you can download for free in PDF format and print freely. We will study the sub-multiples of the unit, the decomposition of a decimal number and the names of the digits. Locating on a graduated line and comparing decimal numbers. We will approach the comparison of two decimal numbers as well as its integer and decimal part in the sixth grade.

I. Sub-multiples of the unit

1. tenths


When you break down a unit into ten equal parts, you get tenths.

A tenth is noted \frac{1}{10}.

In the unit, there are ten tenths so 1=\frac{10}{10}.


2. The hundredths


When you break down a unit into a hundred equal parts, you get a hundredth.

One hundredth is noted \frac{1}{100}.

In the unit, there are one hundredths so 1=\frac{100}{100}.


3. thousandths


When you break down a unit into a thousand equal parts, you get thousandths.

A thousandth is noted \frac{1}{1000}.

In the unit there is one thousandth therefore 1=\frac{1\,000}{1\,000}.



II. Decomposition and name of the numbers


Any number that can be written as a decimal fraction, i.e. whose numerator is a whole number and whose denominator is 1,10,100,1 000,10 000 …, is a decimal number.

It can also be noted using a comma, it is its decimal writing: it is composed

of an integer part and a decimal part.


A decimal number has a finite decimal part.


Consider the decimal number 1345.824.

  • This number reads one thousand three hundred and forty-five units and eight hundred and twenty-four units.
  • It can be broken down into the following form 1\,345,824=,(\,1\times  \,1000\,\,)+\,\,(3\times  \,100\,\,)+\,(\,4\times  \,10\,\,)+\,(\,5\times  \,1\,,)+\,(\,8\times  \,\frac{1}{10}\,\,)+\,(\,2\times  \,\frac{1}{100}\,\,)+,(\,4\times  \,\frac{1}{1\,000}\,\,)
  • Here is the name of each number:
  • 1 is the number of thousands
  • 3 is the number of hundreds
  • 4 is the tens digit
  • 5 is the number of units
  • 8 is the number of tenths
  • 2 is the number of hundredths
  • 4 is the number of thousandths.


An integer is a particular decimal number.

Indeed, 25 can be written with a comma 25=25.0 or as a decimal fraction 25=\,\frac{25}{1}.

III. Locating on a graduated half-line


What are the abscissae of points A and B?

One unit is divided into ten equal parts, which means that it is divided into ten-tenths.

Point A is 2 tenths after 3. So its abscissa is 3+\frac{2}{10}=3,2.

Point B has the abscissa 0+\frac{3}{10}=0,3.

We note A(3,2) and B(0,3).

IV. Comparison and storage

1.comparison of two decimal numbers


Comparing two numbers means finding out which is bigger, or smaller, or telling if they are equal.


We use the symbols > for “greater than” and < for “less than”.


To compare two decimal numbers written in decimal form:

  • we compare the whole parts;
  • if the whole parts are equal, then the tenths numbers are compared;
  • they are equal, so we compare the numbers of the hundredths;
  • they are equal, so we compare the thousandths figures;
  • and so on until the two numbers have different digits.


Compare the numbers 81.357 and 81.36.

  • First, we compare the integer parts of the two numbers;
  • they are equal, so we compare the numbers of the tenths;
  • they are equal, so we compare the numbers of the hundredths.
  • 5<6 so 81.357<81.36.


When the whole parts are equal, the decimal parts can be compared.

81,357=81+\frac{357}{1\,000} and 81,36=81+\frac{36}{100}=81+\frac{360}{1\,000}=81,360.

Now, 360 thousandths is greater than 357 thousandths so 81.36>81.357.

2.2 Arrangement of two decimal numbers


Arrange the numbers 25,342;\,253,42;\,25,243;\,235,42;\,25,324 in ascending order.

The smallest number is found, then the smallest of the remaining numbers, and so on until the last one.

This gives 25,243<25,324<25,342<235,42<253,42.

Have you assimilated the course on decimal numbers in 6th grade?

Les nombres décimaux

QCM de maths en 6ème sur les nombres décimaux.

Things to remember:

Skills to learn about decimal numbers:

what to remember

  • Know the definition of a decimal number;
  • Notion of integer and decimal parts;
  • Know how to give the position of a number (tenth, hundredth, unit, thousands, …);
  • Perform operations (addition, subtraction, multiplication and Euclidean division);
  • Decompose a decimal number;
  • Know how to compare two decimal numbers and place abscissas on a graduated half-line.

This course is in accordance with the official programs of thenational education.

In addition, you can continue with the exercises on decimal numbers in the sixth grade.

Cette publication est également disponible en : Français (French) العربية (Arabic)

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