What Is Expanded Form in Mathematics?

In mathematics, expanded form is a method of representing a number through an addition statement by totaling the values of its digits. For example, the number 3,745 can be written in expanded form as 3,000 + 700 + 40 + 5. A multiplication statement can also be used in expanded form.

The decimal system is the most commonly used number system in mathematics. All numbers can be denoted as a power of 10 by using a combination of the whole number 0 and the first nine integers, which are 1, 2, 3, 4, 5, 6, 7, 8 and 9. These numerical characters are also called numerals or digits.

A place value pertains to the numerical equivalent of a digit based on where it is positioned in a number. For example, the number 14,382 has a 1 in the ten-thousands' place, a 4 in the thousands' place, a 3 in the hundreds' place, an 8 in the tens' place and a 2 in the digits' place.

There are three general ways to express a certain number. These methods are the standard form, word form and expanded form. For instance, the number 7,352 is in standard form. The word form of the number is seven thousand three hundred and fifty two.

To express a number in expanded form, it is first split into its place values. The number 7,352 has seven 1,000s, three 100s, 5 10s and 2 1s. It is then written in expanded notation as 7000 + 300 + 50 + 2.