# Math Lesson 1.1.6 - Classes and Placeholders

Welcome to our Math lesson on Classes and Placeholders, this is the sixth lesson of our suite of math lessons covering the topic of Numbering Systems, a Historical View, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

## Classes and Placeholders

To simplify understanding, numbers are grouped into sets of three digits that start from right to left. These groups are known as classes. Thus, starting from the left we have the simple class, the thousands class, then the millions class, then the billions class and so on. A small space or a comma is often used to separate the classes from each other. The three digits contained in a class are known as placeholders. Thus, for each class we have the placeholder of ones, tens and hundreds. We can see an example of this in the figure below. The above number can be written as 601 843 279 or 601,843,279 and means 603 million 843 thousands and 279. For example, the placeholder containing the digit 4 shows ten thousands, the placeholder containing the digit 1 shows one millions and so on.

### Example 2

What does the digit 4 indicate in the following numbers?

1. 3,248,632
2. 52,113,247
3. 304,618

### Solution 2

1. Since Hindu-Arabic numerals increase by 10 times when moving from right to left, we have 2 for ones, 3 for tens, 6 for hundreds, 8 for one-thousands, 4 for ten-thousands, 2 for hundred thousand and 3 for one millions. Hence, the digit 4 here indicates ten-thousands.
2. Here the digit 4 indicates tens, as it is in the second position from the right.
3. Here the digit 4 indicates one thousands, as it is in the fourth position from the right.

## More Numbering Systems, a Historical View Lessons and Learning Resources

Arithmetic Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
1.1Numbering Systems, a Historical View
Lesson IDMath Lesson TitleLessonVideo
Lesson
1.1.1Egyptian Numerals
1.1.2Babylonian Numerals
1.1.3Mayan Numerals
1.1.4Roman Numerals
1.1.5Hindu-Arabic Numerals
1.1.6Classes and Placeholders

## Whats next?

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7. Continuing learning arithmetic - read our next math tutorial: Number Sets, Positive and Negative Numbers and Number Lines