Place value (T1 W2)
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Place value refers to 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. Understanding place value is crucial for performing arithmetic operations and for comprehending larger numbers. Each position in a number has a value that is ten times greater than the position to its right.
Let's take the number 7,236. We can break this down by place value: The '7' is in the thousands place (7,000), the '2' is in the hundreds place (200), the '3' is in the tens place (30), and the '6' is in the units place (6). So, 7,236 can be expressed as 7,000 + 200 + 30 + 6. This method helps us understand the contribution of each digit to the overall value of the number.
Now, let's practice identifying place values together. Consider the number 5,849. What is the value of the digit '8'? Students should recognize that '8' is in the hundreds place, so its value is 800. Next, what is the value of '4'? It is in the tens place, giving it a value of 40. Work through several examples as a class, encouraging students to explain their reasoning and use visual aids like place value charts.
Now it's your turn to practice independently. Solve the following problems: 1) What is the value of the digit '3' in the number 3,472? 2) Break down the number 9,105 into its place values. 3) Write the number represented by 6,000 + 500 + 40 + 2. Make sure to show your working clearly for each problem.
Answer: 5,000
The digit '5' is in the thousands place, which means it represents 5,000.
Answer: 300
The digit '3' is in the hundreds place, so its value is 300.
Answer: 3,170
In the number 3,170, the '7' is in the tens place.
Answer: 9,000
The digit '9' is in the thousands place, representing 9,000.
Answer: 4,000 + 200 + 5
The expanded form of 4,205 is 4,000 + 200 + 5.
Answer: 5,634
Adding the values together gives us the number 5,634.
Answer: 200
The digit '2' is in the hundreds place, so its value is 200.
Answer: 8,000 + 900 + 10
The breakdown shows the contribution of each digit to the overall number.