There exists many different number systems. Number systems you might know already are the sexagesimal system with the number 60 as its base which is used to tell time, or the decimal system with the number 10 as base which is used for the real number line. This entry will teach you about the decimal system, which is the most commonly used system in our part of the world.

So what is the decimal system? It has the ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Since all the numbers on the real number line are made up of one or more of these ten digits, we call the number system the decimal system. Decimal means “based on ten”.

Below, all the numbers from 0 up to and including 100 are listed. Let’s look at the structure. The first row only consists of the 10 digits. The next rows consist of numbers that are put together by two digits, except the number 100, which has three digits. When you use the digits to write larger or smaller numbers, you’re affected by the place value system.

The numbers on the first row all are all in the ones place. When you put together several digits, you must use more of the places. For the numbers from 0 up to and including 100 you use ones, tens and hundreds.

In the second row, you can see that there’s always the number 1 in the tens place, and in the ones place the numbers start with 0 and end with 9 across the row. In the third row, there’s always the number 2 in the tens place, and in the ones place the numbers start with 0 and end with 9 when reading from left to right. It continues like this from one row to the next until you’ve used all the digits from and including 1 to and including 9 in the tens space.

When all the digits are used in the tens, you start using the hundreds. You start with the number 1 in the hundreds. Since you have to use all the digits, 0 must also be included. This is the first of our digits, so 0 is the first number you put in the tens and ones. Then you have arrived at the number 100. We can say that you recycle the digits to make numbers.

Think About This

Here you have all the numbers from 0 to 100:

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |

10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |

20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 |

30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 |

40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |

50 | 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 |

60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 |

70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 |

80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |

90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 |

100 | |||||||||

Math Vault

Want to solve exercises about decimal numbers? Try Math Vault!