Place value (T3 W8)
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Place value is the value of a digit based on its position in a number. For example, in the number 4,582, the digit 4 is in the thousands place, meaning it represents 4,000. Each position in a number has a different value: the ones, tens, hundreds, thousands, and so on. Understanding place value is crucial for performing arithmetic operations and comparing numbers.
Let's take the number 7,236. The digit 7 is in the thousands place, so its value is 7,000. The digit 2 is in the hundreds place, giving it a value of 200. The digit 3 is in the tens place, which means it represents 30, and the digit 6 is in the ones place, representing 6. Therefore, we can break down the number as follows: 7,236 = 7,000 + 200 + 30 + 6.
Now, let's use base ten blocks to represent the number 5,431. Using blocks, we can show 5 thousands blocks, 4 hundreds blocks, 3 tens blocks, and 1 ones block. As a class, we will build this number using the blocks and then write it in expanded form: 5,431 = 5,000 + 400 + 30 + 1. Discuss how each block corresponds to the value of its position.
Now it's your turn! Solve the following problems on your own: 1. Write the number 3,205 in expanded form. 2. Identify the place value of the digit 8 in the number 48,672. 3. What is the value of the digit 6 in the number 6,789? Show your working clearly for each problem.
Answer: 9,000
The digit 9 is in the thousands place, which means it represents 9,000.
Answer: 600
The digit 6 is in the hundreds place, so its value is 600.
Answer: 4,000 + 300 + 20 + 1
In expanded form, each digit is represented by its place value.
Answer: 300
The digit 3 is in the hundreds place, which means it represents 300.
Answer: Thousands place
The digit 7 is in the thousands place, indicating its value is 7,000.
Answer: 3
In the number 8,234, the digit 3 is in the tens place.
Answer: 2,000
The digit 2 is in the thousands place, so its value is 2,000.
Answer: 56
The number 5,600 contains 56 hundreds.