When discussing integers, standard form refers to an integer written as a number, while word form describes an integer written out as a word. Expanded form uses different numbers in an equation to express the integer.
Examples of numbers written in standard form are "543" and "1,351." Standard form is the numerical form most often used in equations and general mathematics. Examples of numbers written in word form are "twelve," "five hundred forty-three" and "one thousand five hundred fifty-one." All compound numbers between 21 and 99 are hyphenated when written in word form. The word "and" is not necessary when writing out whole numbers; it is necessary when writing out a number with digits to the right of a decimal point.
Expanded form consists of breaking down a number by degrees of place value. For example, the number "1,351" in expanded form is "1,000 + 300 + 50 + 1." Usually, the place values are arranged from greatest to least. Teachers typically use this form as a way to teach students about place value.
Standard form has a slightly different meaning in algebra. When referring to basic equations, standard form refers to an equation that equals zero. When referring to polynomials, standard form refers to arranging the terms from highest to lowest degree.