Math Lesson 1.7.2 - Place Values and Classes

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Welcome to our Math lesson on Place Values and Classes, this is the second lesson of our suite of math lessons covering the topic of Decimal Number System and Other Numbering Systems, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

Place Values and Classes

We explained in tutorial 1.1 that digits in decimal system numbers are organized in groups of three, where each group is called class. Moving from right to left we have the simple class, then the thousands class, then the millions class, then the billions one and so on. Moreover, each class contains three digits, known as place values (the corresponding position is known as the placeholder). Starting from right to left, place values represent units (ones), tens and hundreds of the corresponding class. Numbers in the decimal system increase 10 by 10 when moving from left to right. Hence, the classes and place values of the number 501,647,390,528 are as follows

For example, the digit 6 is in the millions class and shows the value of hundreds of this class. Hence, we say the digit 6 shows how many hundreds of millions the original number has.

We can write the above number in disassembled form as:

Example 2

What is the power of ten indicated by the digits 3 and 5 in the number 38,542,400?

Solution 2

We must can write the number in the decomposed form to understand better what do the digits 3 and 5 indicate. We have

Hence, the digit 3 indicates the 7th power of ten while the digit 5 indicates the 5th power of ten.

Based on the structure of decimal numbers, we can find any missing digit if we know any relationship with the other digits of the number. Let's consider an example.

Example 3

When the digits of a 2-digit number are inverted, we obtain a number that is 63 greater than the original number. What is/are the possible original number/s?

Solution 3

If we denote the original number by ab, we have

Since the value indicated by a digit in the tens place value is 10 times greater than that indicated by the same digit in the units place value, we can write

We can bring everything to the left side by changing the sign to the elements on the right (we will explain why we do this when dealing with equations in chapter 9; for now we are taking this rule as granted).

We can factorize 9 as a common factor:

Hence, the possible combinations for a and b are a = 9 and b = 2 or a = 8 and b = 1. Therefore, the possible original numbers are 92 or 81.

In the following paragraph, we will take a look at other number systems and how to do operations with them. Likewise, you will learn how to convert a number from one system into another. For illustration, we will consider the base 2 and base 16 number systems but all the other systems work in the same way.

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2. Arithmetic Math tutorial: Decimal Number System and Other Numbering Systems. Read the Decimal Number System and Other Numbering Systems math tutorial and build your math knowledge of Arithmetic
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4. Arithmetic Revision Notes: Decimal Number System and Other Numbering Systems. Print the notes so you can revise the key points covered in the math tutorial for Decimal Number System and Other Numbering Systems
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6. Check your calculations for Arithmetic questions with our excellent Arithmetic calculators which contain full equations and calculations clearly displayed line by line. See the Arithmetic Calculators by iCalculator™ below.
7. Continuing learning arithmetic - read our next math tutorial: Numbering Systems, a Historical View

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