Place value (T3 W8)
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Place value is 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. Similarly, the digit 5 is in the hundreds place, representing 500. Understanding place value helps us read, write, and compare numbers accurately. In decimal numbers, the place value extends to tenths, hundredths, and so on, which is crucial for understanding fractions and measurements.
Consider the number 7,203. To 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). Therefore, the value of the number can be expressed as 7,000 + 200 + 0 + 3. In decimal form, for the number 45.678, the 4 is in the tens place (40), the 5 is in the units place (5), the 6 is in the tenths place (0.6), the 7 is in the hundredths place (0.07), and the 8 is in the thousandths place (0.008).
Let's practice identifying place values together. Write the number 3,456 on the board. Ask students to identify the place value of each digit. The 3 is in the thousands place, the 4 is in the hundreds place, the 5 is in the tens place, and the 6 is in the units place. Next, present the number 12.345 and have students identify the place values of the digits after the decimal point. This will reinforce their understanding of both whole numbers and decimals.
Now, it's your turn to practice independently. Solve the following problems: 1) What is the place value of the digit 9 in the number 9,876? 2) Write the number 0.456 in expanded form. 3) Identify the value of the digit 2 in the number 52.789. Show your working clearly for each problem.
Answer: 500
The digit 5 is in the hundreds place, which represents 500.
Answer: 0.08
The digit 8 is in the tenths place, which represents 0.08.
Answer: 3,000 + 200 + 10
The expanded form breaks down the number into its place values.
Answer: 700
The digit 7 is in the hundreds place, which represents 700.
Answer: 4
The digit 4 is in the tens place, representing 40.
Answer: 3,456
In the number 3,456, the digit 3 is indeed in the thousands place.
Answer: 0.05 + 0.006
The expanded form shows the value of each digit in the decimal.
Answer: 200
The digit 2 is in the hundreds place, which represents 200.