Place value (T2 W10)
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Place value is the value of a digit depending 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 to the right decreases in value by a factor of ten. Understanding place value is crucial for performing arithmetic operations and for understanding the size of numbers.
Consider the number 6,731. Here, '6' is in the thousands place (6,000), '7' is in the hundreds place (700), '3' is in the tens place (30), and '1' is in the units place (1). To find the total value, we can add these values together: 6,000 + 700 + 30 + 1 = 6,731. This breakdown helps us see how each digit contributes to the overall value of the number.
Let's practice identifying place values together. Write the number 5,294 on the board. Ask students to identify the place value of each digit. Discuss as a class: 'What is the value of the digit '5'? What about '2'?'. Encourage students to explain their reasoning and use visual aids like place value charts to reinforce their understanding.
Now it's your turn! Solve the following problems independently. 1. What is the place value of the digit '8' in the number 48,362? 2. Write the number 3,205 in expanded form. 3. If you add 1,000 to the number 2,456, what is the new number? Show your working clearly. Remember to check your answers and correct any mistakes.
Answer: 300
The digit '3' is in the hundreds place, which represents 300.
Answer: 4,150
In the number 4,150, the '5' is in the tens place.
Answer: 7,000 + 800 + 90 + 0
Expanded form breaks down the number into the sum of its place values.
Answer: 9,000
The digit '9' is in the thousands place, representing 9,000.
Answer: 1,300
Subtracting 200 from 1,500 gives you 1,300.
Answer: 5
The digit '5' is in the thousands place, representing 5,000.
Answer: 2,000
The digit '2' is in the thousands place, which is worth 2,000.
Answer: 60
The digit '6' is in the tens place, representing 60.