Expanded Form Calculator

Every standard number relies on a base-ten positional system where each digit's value depends on its position. The expanded form explicitly displays this value by breaking a number into an addition expression of its digits multiplied by their respective place values, such as thousands, hundreds, tens, ones, tenths, and thousandths. For instance, a number like abc.de is represented algebraically as (a × 100) + (b × 10) + (c × 1) + (d × 0.1) + (e × 0.01). The calculator processes your input by isolating each digit via mathematical modulo and division operations, mapping them directly to their corresponding power of ten.

Let us find the expanded form of the decimal number 709.104. First, separate the whole number part from the decimal part. The whole number 709 consists of 7 hundreds, 0 tens, and 9 ones. Written out, this is (7 × 100) + (0 × 10) + (9 × 1). Next, evaluate the fractional part 0.104, which contains 1 tenth, 0 hundredths, and 4 thousandths, written as (1 × 0.1) + (0 × 0.01) + (4 × 0.001). Combining both segments gives the complete expanded notation: 700 + 0 + 9 + 0.1 + 0 + 0.004, or expressed with multiplication: (7 × 100) + (9 × 1) + (1 × 0.1) + (4 × 0.001).

When writing numbers in expanded form manually, you can choose to skip digits with a value of zero to keep your expression concise (e.g., writing 709 as 700 + 9 instead of 700 + 0 + 9). However, keeping the zeros can be helpful when learning the absolute position of each digit. Always double-check your decimal places, as mixing up tenths (0.1) and thousandths (0.001) is the most common error in calculations.