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Purcell Math

Math Methods Grades 4-8

Understanding Place Values: Breaking Down Large Numbers

Introduction

Place values are essential for understanding the magnitude of each digit in a number, especially in large or decimal numbers. Each position in a number represents a different power of ten, helping us read and interpret numbers accurately. Let’s explore place values using an example.

Core Concepts:

1. Identifying Place Values in Whole Numbers:
Every digit in a whole number has a specific place value, which multiplies its value by a power of ten. For example, in the number 123,456:
6 is in the ones place
5 is in the tens place
4 is in the hundreds place
3 is in the thousands place
2 is in the ten thousands place
1 is in the hundred thousands place

2. Decimal Place Values:
When we move to decimals, the values of each position change. Starting from the decimal point:
7 is in the tenths place
8 is in the hundredths place
9 is in the thousandths place
0 is in the ten thousandths place
The second 1 is in the hundred thousandths place
The second 2 is in the millionths place

3. Reading and Understanding Decimals:
Each place to the right of the decimal point divides the value by ten, allowing us to understand even the smallest parts of a number.

Conclusion

Knowing place values allows us to read, interpret, and work with numbers of all sizes. By mastering place values, we make calculations simpler and gain a clearer understanding of numbers in everyday situations.

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