Place value (T2 W10)
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Place value refers to the value of a digit based on its position within a number. For example, in the number 4,582, the digit '4' is in the thousands place, meaning it represents 4,000. Understanding place value is crucial for performing operations like addition, subtraction, and even multiplication and division. Each position in a number has a specific value, which increases by a factor of ten as you move left and decreases by a factor of ten as you move right.
Consider the number 7,203. To identify the place value of each digit, we can break it down: The '7' is in the thousands place (7,000), the '2' is in the hundreds place (200), the '0' is in the tens place (0), and the '3' is in the units place (3). Thus, the value of 7,203 can be expressed as 7,000 + 200 + 0 + 3. This breakdown helps us understand how each digit contributes to the overall value of the number.
Let's practice identifying place values together. Take the number 5,648. What is the value of the digit '6'? Students should recognize that '6' is in the hundreds place, representing 600. Now, what about the digit '4'? It is in the tens place, representing 40. Work through a few more examples as a class, asking students to identify the place value of different digits in various numbers.
Now it's your turn to work independently. Solve the following problems: 1) What is the place value of '9' in the number 9,482? 2) Write the number 3,205 in expanded form. 3) Identify the digit in the tens place of the number 6,731. Show your working clearly for each problem.
Answer: 300
The digit '3' is in the hundreds place, which represents 300.
Answer: Hundreds
The digit '9' is in the hundreds place, representing 900.
Answer: 2,000 + 0 + 10 + 4
In expanded form, each digit is represented by its place value.
Answer: 5,000
The digit '5' is in the thousands place, representing 5,000.
Answer: 2
The digit '2' is in the tens place, representing 20.
Answer: 8
The digit '8' is in the tens place, representing 80.
Answer: 0
The digit '0' in the hundreds place does not contribute to the value.
Answer: 5
The number 12,345 has five digits: 1, 2, 3, 4, and 5.