How Do You Write a Number in Expanded Notation?


Quick Answer

To write a number in expanded notation, rewrite it as a sum of its various place values. This shows the value of each digit in the number. For example, the number 123 can be written in expanded notation as 123 = 100 + 20 + 3.

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Full Answer

There are two acceptable ways to rewrite a number in expanded notation. One way to write 326 in expanded notation is: 326 = 300 + 20 + 6. In this method, three is in the hundreds place because we wrote it as 300, and two is in the tens place, because we wrote it as 20.

Another way to rewrite a number in expanded notation would be to take the previous method a step further, and write it as a sum of multiples. For example, 1,776 in this method expanded notation would look like this: 1,776 = (1 x 1000) + (7 x 100) + (7x 10) + (6 x 1).

A third way is to rewrite the above method as multiples for the powers of ten, which represent the place of each number in the digit: 1,776 = (1 x 10^3) + (7 x 10^2) + (7 x 10^1) + (6 x 10^0).

Numbers with decimals can also be rewritten in expanded notation. Here is an example of how: 101.205 = (1 x 100) + (1 x 1) + (2 x 1/10) + (5 x 1/100).

The number of zeros in the denominator for the decimal digits is the same as the number of places from the decimal point in the number. For example, the denominator for 5 in the above number is 100. Since 5 is two places from the decimal point, there are two zeros in its denominator (100).

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