Lesson 1: Place Value Patterns and Powers of 10

Property

Each place represents 10 times the place just to the right. A number is a sequence of digits, and its value is the sum of each digit multiplied by its place value (a power of ten). For example:

This can also be written using exponents:

Examples

• The number 5,281 in expanded form is $5 \times 1000 + 2 \times 100 + 8 \times 10 + 1$.
• The number 709 shows the importance of zero as a placeholder. It is $7 \times 100 + 0 \times 10 + 9$.
• A larger number like 4,600 is written as $4 \times 1000 + 6 \times 100 + 0 \times 10 + 0 \times 1$.

Explanation

Place value is like a secret code where a digit's position tells you its real worth. A 7 in the tens place is 70, but in the hundreds place, it's 700! This system lets us write any number, big or small.

Property

Each place value unit is 10 times greater than the unit to its immediate right.
This creates a multiplicative relationship where one of a larger unit can be decomposed into ten of the next smaller unit.

Examples

Property

Each place value is 10 times greater than the place value to its immediate right.
Therefore, multiplying a number by 10 shifts each of its digits one place to the left, increasing the number's total value by a factor of 10.

Examples