Place Value of a Number

Place Value of a Number

Digits and Their Values

• Definition: Place value refers to the value of a digit based on its position within a number.
• Digits: The basic symbols used in numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• Value by Position:
  • Each digit has a value determined by its position (units, tens, hundreds, etc.).
  • Rightmost digit: Represents units (1s).
  • Second digit from the right: Represents tens (10s).
  • Third digit from the right: Represents hundreds (100s).
  • Continuing left: Each position increases by a power of 10 (thousands, ten thousands, etc.).

Expanded Form

• Definition: Expanded form expresses a number as the sum of the values of its digits.
• Format: Each digit is multiplied by its place value.
• Example:
  • For the number 345:
    • 3 is in the hundreds place → 3 × 100 = 300
    • 4 is in the tens place → 4 × 10 = 40
    • 5 is in the units place → 5 × 1 = 5
  • Expanded form: 300 + 40 + 5
• Purpose: Helps to understand the value of each digit and reinforces the concept of place value.

Place Value of a Number

Digits and Their Values

• Place value is the value of a digit based on its location within a number.
• Basic symbols used in numbers are digits: 0 through 9.
• Each digit's value is determined by its position, such as units, tens, hundreds, etc.
• The rightmost digit indicates the units or ones place.
• The second digit from the right corresponds to the tens place (10s).
• The third digit from the right signifies the hundreds place (100s).
• Each position to the left of the rightmost digit represents increasing powers of 10, progressing to thousands, ten thousands, and beyond.

Expanded Form

• Expanded form expresses a number as the sum of the values of its individual digits.
• In expanded form, each digit is multiplied by its corresponding place value.
• Example for the number 345:
  • The digit 3 is in the hundreds place, contributing 3 × 100 = 300.
  • The digit 4 is in the tens place, contributing 4 × 10 = 40.
  • The digit 5 is in the units place, contributing 5 × 1 = 5.
• Hence, the expanded form of 345 is written as 300 + 40 + 5.
• Understanding expanded form reinforces the concept of place value and illustrates the contribution of each digit to the overall number.

This quiz covers the concept of place value and how it determines the value of digits in a number based on their positions. It also includes the definition of expanded form and demonstrates how to express numbers as the sum of their digit values. Perfect for students learning basic number theory.