Place Value

Definition

Place value is a fundamental concept in mathematics that describes the value of a digit based on its position within a number. It determines the worth of each digit in a number, whether it represents ones, tens, hundreds, or any other power of ten.

5 Must Know Facts For Your Next Test

1. Place value determines the worth of each digit in a number, with the rightmost digit representing ones, the next digit representing tens, the next digit representing hundreds, and so on.
2. Understanding place value is essential for performing operations like addition, subtraction, multiplication, and division with whole numbers and decimals.
3. The decimal numeral system, which uses the digits 0-9, is the most common place value system, with each digit's value determined by its position relative to the decimal point.
4. In the decimal system, the value of a digit increases by a factor of 10 as you move one place value to the left, and decreases by a factor of 10 as you move one place value to the right.
5. Expanded notation is a way of writing a number that shows the value of each digit based on its place value, which can help visualize and understand the concept of place value.

Review Questions

• Explain how place value is used to represent and understand whole numbers.
  • Place value is essential for representing and understanding whole numbers. In the decimal system, the rightmost digit represents the ones place, the next digit to the left represents the tens place, the next digit the hundreds place, and so on. This means that the value of each digit is determined by its position within the number. For example, in the number 4,523, the 4 represents 4 thousands, the 5 represents 5 hundreds, the 2 represents 2 tens, and the 3 represents 3 ones. Understanding place value is crucial for performing operations like addition, subtraction, multiplication, and division with whole numbers.
• Describe how place value is used to represent and understand decimal numbers.
  • Place value is also crucial for representing and understanding decimal numbers. In the decimal system, the digits to the right of the decimal point represent fractional values, with each digit's value decreasing by a factor of 10 as you move from right to left. For example, in the number 4.523, the 4 represents 4 whole units, the 5 represents 5 tenths, the 2 represents 2 hundredths, and the 3 represents 3 thousandths. Understanding the place value of each digit in a decimal number is essential for performing operations like addition, subtraction, multiplication, and division with decimal numbers.
• Analyze how the concept of place value can be used to convert between different numeral systems, such as between decimal and expanded notation.
  • The concept of place value can be used to convert between different numeral systems, such as between decimal and expanded notation. In expanded notation, a number is written to show the value of each digit based on its place value. For example, the number 4,523 in expanded notation would be written as 4 × 1,000 + 5 × 100 + 2 × 10 + 3 × 1. This demonstrates the place value of each digit, with the 4 representing 4 thousands, the 5 representing 5 hundreds, the 2 representing 2 tens, and the 3 representing 3 ones. Conversely, the expanded notation can be used to write the number in standard decimal form by adding up the values of each place value. Understanding place value is the key to being able to convert between different numeral systems and representations of a number.

Related terms

Digit: A single symbol used to represent a number, such as 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.

Numeral System: A system for representing numbers, such as the decimal (base 10) system, which uses the digits 0-9.

Expanded Notation: A way of writing a number that shows the value of each digit based on its place value, such as 4,523 = 4 × 1,000 + 5 × 100 + 2 × 10 + 3 × 1.