In mathematics, standard form and expanded form are two ways of representing numbers. Converting between the two forms is an important skill in elementary mathematics. Here’s a short explanation of each form:

  1. Standard Form: Standard form, also known as the “usual” or “normal” form, represents a number using digits. It is the most common way to write numbers. For example, the number 547 is in standard form.
  2. Expanded Form: Expanded form represents a number as the sum of its place values. It breaks down a number into its individual digits and their corresponding place values. For example, the number 547 in expanded form would be written as (500 + 40 + 7).

Converting from standard to expanded form: To convert a number from standard form to expanded form, you break it down into its individual digits and write each digit multiplied by its corresponding place value. For example, to convert 547 to expanded form:

  • The digit 5 is in the hundreds place, so it is multiplied by 100 (5 x 100 = 500).
  • The digit 4 is in the tens place, so it is multiplied by 10 (4 x 10 = 40).
  • The digit 7 is in the ones place, so it remains as it is (7 x 1 = 7).
  • Add the results together: 500 + 40 + 7 = 547.

Converting from expanded to standard form: To convert a number from expanded form to standard form, you add up the values of the expanded form expression. For example, to convert (300 + 20 + 5) to standard form:

  • Add the values together: 300 + 20 + 5 = 325.

These are the basics of converting between standard and expanded form. Understanding these concepts will help you work with numbers more effectively and develop a deeper understanding of place value.