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Questions and Answers
A three-digit number can be broken down into thousands, hundreds, tens, and ones positions, each represented by specific place values with unique symbols: - ______ position: Symbolized by 'K', 'M', or 'B'.
A three-digit number can be broken down into thousands, hundreds, tens, and ones positions, each represented by specific place values with unique symbols: - ______ position: Symbolized by 'K', 'M', or 'B'.
Thousands
For instance, 389 ______ is 389 imes 10^2 = 38,900.
For instance, 389 ______ is 389 imes 10^2 = 38,900.
Hundreds
217 ______ is 21 imes 10 = 210.
217 ______ is 21 imes 10 = 210.
Tens
Forty-three ones is 43 imes 1 = ______.
Forty-three ones is 43 imes 1 = ______.
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6 ______ are equivalent to 6,000,000.
6 ______ are equivalent to 6,000,000.
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1 ______ is equivalent to 1,000.
1 ______ is equivalent to 1,000.
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In the number 907, the expanded form is 9 x 100 + 0 x 10 + 7 x ______
In the number 907, the expanded form is 9 x 100 + 0 x 10 + 7 x ______
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Commutativity states that 123 is ______ than 321.
Commutativity states that 123 is ______ than 321.
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In the comparison 29 + 2 x 10^1 ______ 31 x 10^1.
In the comparison 29 + 2 x 10^1 ______ 31 x 10^1.
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The Zero Property of Addition states that 40 - 34 = ______.
The Zero Property of Addition states that 40 - 34 = ______.
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In the comparison 712 > 709, the hundreds column shows that 1 is ______ than 0.
In the comparison 712 > 709, the hundreds column shows that 1 is ______ than 0.
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In the comparison 967 < 998, the hundreds column shows that 6 is ______ than 9.
In the comparison 967 < 998, the hundreds column shows that 6 is ______ than 9.
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Study Notes
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.
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Description
Explore the representation of three-digit numbers using base-ten numerals, number names, and expanded forms. Learn how to compare numbers by understanding place value properties like commutativity and zero property of addition.
