As illustrated below and by other available expanded form solutions, this application will convert a number in standard form to expanded form with the aid of a place value chart.
Students in the 3rd grade should be able to convert a number in standard form to expanded form up to 1,000 under Common Core standards. The expanded form of a number is written as the sum of the place values of its digits. In other words, the ability to find the place values of the digits in a number is necessary to convert a number in standard form to expanded form.
There are multiple ways of expressing the place value of a digit. The most common way of expressing the place value of a digit is as the product of the digit times the value or multiplier corresponding to the place it occupies in the number. For example, 60 is the product of 6 * 10, and it is also the place value of 6 in 265 since 6 occupies the Tens place.
The place value of a digit that is part of a decimal number could be expressed as a fraction or decimal. For example, 1/10 = 0.1. And the place value of a digit could be expressed in scientific notation. Since 102 = 100, the 4 in 425 could be expressed as 4 * 102. Notably, if a digit equals 0 in a number, it is considered a 0 placeholder, and 0 placeholders are not included in the expanded form of a number.
Because there are multiple ways of expressing the place value of a digit, there are multiple ways of expressing the sum of the place values of all the digits or the expanded form of the number. As illustrated with the example of 37.24 below, the application above will convert a number in standard form to expanded form by expressing the number entered as the sum of the place values of the digits expressed as products, as a sum of the quantities that produce the resulting product, and as a sum of the place values expressed in scientific notation. As the case with 37.24, it will also return the expanded form of the number entered as the sum of the place values expressed as fractions and decimals. In all cases, the sum of the place values must equal the number entered.
