What are decimal numbers?

The decimal numbers are used to represent smaller numbers than unity.

Decimal numbers are written to the right of the Units separated by a comma. That is to say:

Hundreds Tens Units, Tenths Hundreds Thousands

In the image below, the first square represents Unity . If we divide this unit into 10 equal parts (second square), we will represent the Tenths . If we divide the tenths into 10 equal parts or the unit into 100 equal parts (third square), we will represent the Hundredths .

Let’s see some examples
  • First example:If we divide the unit into 10 equal parts, we will have tenths. And we have colored 7 of these parts. The way to write it is 0 units, 7 tenths = 0.7
  • Second example : In the second example we also have tenths and we have colored 1. It will be written as follows: 0 units, 1 tenth = 0.1
  • Third example : In the third example we have hundredths represented, of which we have 6 tenths and 4 hundredths colored. Therefore it will be written: 0 units, 6 tenths 4 hundredths = 0.64
  • Fourth example: We have hundredths (the unit among 100), of which we have colored 3 tenths and 5 hundredths. We will write it: 0 units, 3 tenths 5 hundredths = 0.35
  • Fifth example: We have two colored whole units and the third unit, which is divided into hundredths, we have 8 colored tenths and one colored hundredth. Therefore, it will be written: 2 units, 8 tenths 1 hundredths = 2.81
What is the relationship of decimals to fractions?
  • The Unit is represented by 1
  • The Tenth is the unit divided into 10 equal parts = 1/10 = 0.1
  • The hundredth is the unit divided into 100 equal parts = 1/100 = 0.01
  • The thousandth is the unit divided into 1000 equal parts = 1/1000 = 0.001
Example to go from decimal to fraction:


We look at the last number, at 8, which takes the place of thousandths, therefore the denominator will have to be 1000. And in the numerator we will write the complete number without the comma. 7,508 = 7508/1000

Example to go from fraction to decimal:


Since the denominator is 100, the last number in the numerator (the 2) must be the hundredths, the previous one (the 0) must be the tenths and the previous one (the 4) must be the units, putting the eat behind the units. Therefore 402/100 = 4.02

This is part of the explanation that you can see in the tutorial of introduction to decimals . I encourage you to see it in full by clicking on the link.

Below we offer you  online exercises to practice the decimal numbers in primary school in a fun way. We hope you like them.

  • Basic decimal number concept
  • Advanced decimal number concept
  • Decimal concept on a line of numbers

If you want to continue learning about decimal numbers and elementary math, sign up for Smartick and try it for free.


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