Reading and Writing Three-Digit Numbers

Reading and Writing Base-Ten Numbers up to 1000

As we delve into the world of place value beyond ten, our quest for understanding numerical literacy extends towards three-digit numbers. Let's explore how to represent these larger figures using base-ten numerals, their corresponding number names, and expanded forms.

Representing Three-Digit Numbers

A three-digit number can be broken down into thousands, hundreds, tens, and ones positions, each represented by specific place values with unique symbols:

• Thousands position: Symbolized by 'K', 'M', or 'B'. For example, (1\text{ K} \equiv 1,!000), (6\text{ M} \equiv 6,!000,!000).
• Hundreds position: A digit from one to nine followed by the letter 'H'. For instance, (389\text{ H} \equiv 389 \times 10^2 = 38,!900).
• Tens position: Digits from zero to nine. For example, (217) tens is (21 \times 10 = 210).
• Ones position: Single digits between zero and nine. For example, forty-three ones is (43 \times 1 = 43).

Number Names and Expanded Forms

Number names provide us with a verbal representation of three-digit numbers. Here's a list of some common examples:

[ \begin{array}{ccc|l} \text{# in xxx}& \rightarrow & \text{name} &\rightarrow \ \hline 123& \rightarrow & \text{one hundred twenty-three}& \text{(one + two hundreds + three tens)}\ 907& \rightarrow & \text{nine hundred seven}&\ 102&\rightarrow & \text{one thousand two} & \text{(one thousand + two tens)} \end{array} ] The expanded form provides another method of representing large numbers through addition. For instance, (907 = 9 \times 100 + 0 \times 10 + 7 \times 1).

Comparison Using Place Value Properties

When comparing three-digit numbers, it's essential to understand the meaning behind the individual digits. We can utilize properties such as:

• Commutativity: (123 > 321 \Rightarrow 213 > 132).
• Associativity: ((29 + 2) \times 10^1 = 31 \times 10^1 = 3,!100 > 2,!800).
• Zero Property of Addition: (40 - 34 = 6 > 4).

By applying these principles, you will find the correct result when comparing three-digit numbers using the >, =, and < symbols.

For instance, let's examine the comparison (712 > 709): Since both thousands digits ((7)) are equal, we move onto the hundreds column where (1 > 0). Therefore, (712 > 709). Similarly, the comparison (967 < 998) because (6 < 9) in the hundreds column and (7 < 9$ in the ones column.