Skill: Write whole numbers in expanded notation

Expanded notation shows the value of each digit in a whole number. To write a number this way:

1. Identify each digit’s place value.
2. Multiply each digit by its place value.
3. Add the nonzero place-value contributions.

Example: Write $508{,}204$ in expanded notation.

First, identify the value of each digit:

• $5$ is in the hundred-thousands place: $500{,}000$
• $0$ is in the ten-thousands place: $0$
• $8$ is in the thousands place: $8{,}000$
• $2$ is in the hundreds place: $200$
• $0$ is in the tens place: $0$
• $4$ is in the ones place: $4$

The zeros are placeholders. They show that there are no ten-thousands or tens in the number.

Now write the sum of the place-value contributions:

$$508{,}204=500{,}000+8{,}000+200+4$$

You can also write this using powers of $10$:

$$508{,}204 =5\times10^5+8\times10^3+2\times10^2+4\times10^0$$

The terms with zero digits are left out because they add $0$.