Place value (T1 W2)
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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, which means it represents 4,000. Understanding place value is crucial for performing operations such as 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 7,306. To identify the place value of each digit, we can break it down: The '7' is in the thousands place (7,000), the '3' is in the hundreds place (300), the '0' is in the tens place (0), and the '6' is in the units place (6). Therefore, the total value of the number can be expressed as 7,000 + 300 + 0 + 6 = 7,306.
Let's practice identifying place values together. Take the number 5,214. What is the value of the digit '2'? Students should recognize that '2' is in the hundreds place, so its value is 200. Now, what about the digit '1'? It is in the tens place, giving it a value of 10. Continue this process with the class, asking them to identify the values of each digit in various numbers.
Now it's your turn! Solve the following problems independently: 1) What is the value of the digit '6' in the number 6,789? 2) Write the number 4,205 in expanded form. 3) Identify the place value of '9' in the number 9,432. Show your working clearly for each problem.
Answer: 500
The digit '5' is in the hundreds place, which represents 500.
Answer: 400
The digit '4' is in the hundreds place, so its value is 400.
Answer: 2000 + 100 + 50 + 0
Expanded form breaks down the number into the sum of its place values.
Answer: 8000
The digit '8' is in the thousands place, representing 8000.
Answer: 3,000
The digit '3' is in the thousands place, so its value is 3,000.
Answer: 9
In the number 7,891, '9' is in the tens place.
Answer: 0
The digit '0' is in the tens place, which means it has no value.
Answer: 5
The number 12,345 has five digits.