Building on the ideas from Round and PlaceValue, let us learn about expanded notation. Numbers written in expanded notation are grouped by ones, tens, thousands, and so on.

Parentheses in standard notation are helpful, but not required. The number 1974 can be thought of or written as (1 x 1000) + (9 x 100) + (7 x 10) + (4 x 1).

Or 1974 can be written as 1 x 1000 + 9 x 100 + 7 x 10 + 4 x 1. The digits are grouped with (or multiplied by) their place value first, and then added together.

Let us try an example. What is (4 x 1000) + (7 x 100) + (9 x 10) + (1 x 1)?

The answer is 4 thousand, 7 hundred, ninety, and one. We write this as 4791.

We must not be confused if the place values are given to us out of order. For example, 4791 could also be written as (9 x 10) + (4 x 1000) + (1 x 1) + (7 x 100).

Expanded notation can also apply to decimals. Try (3 x 1) + (1 x 0.1) + (4 x 0.01) x (1 x 0.001) x (6 x 0.0001). The answer is 3.1416, which is an approximation of Pi (π).

Parentheses in standard notation are helpful, but not required. The number 1974 can be thought of or written as (1 x 1000) + (9 x 100) + (7 x 10) + (4 x 1).

Or 1974 can be written as 1 x 1000 + 9 x 100 + 7 x 10 + 4 x 1. The digits are grouped with (or multiplied by) their place value first, and then added together.

Let us try an example. What is (4 x 1000) + (7 x 100) + (9 x 10) + (1 x 1)?

The answer is 4 thousand, 7 hundred, ninety, and one. We write this as 4791.

We must not be confused if the place values are given to us out of order. For example, 4791 could also be written as (9 x 10) + (4 x 1000) + (1 x 1) + (7 x 100).

Expanded notation can also apply to decimals. Try (3 x 1) + (1 x 0.1) + (4 x 0.01) x (1 x 0.001) x (6 x 0.0001). The answer is 3.1416, which is an approximation of Pi (π).