Numerals are a way of symbolizing quantities. Writing out a number in its expanded form means that you break down the digits to show what each represents. Our numeral system uses a base-10 system, with 10 distinct symbols for whole quantities from zero to nine. You can combine the numeral symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to represent every possible quantity. Each digit represents a placeholder, which has a name, allowing you to write it out in expanded form.

### Step 1

Learn what each numeral to the left of the decimal represents. The first digit to the left of the decimal point in any number, for example, is the ones, because it represents the number of ones included in the number. The second digit to the left is called the tens, because it represents the number of tens included in that number. The third digit to the left of the decimal is hundreds, because it represents the number of hundreds included in the number.

### Step 2

Learn what each numeral to the right of the decimal represents. The first digit to the right of the decimal point in any number, for example, is the tenths, because it represents the proportion out of 10 equal parts of a whole. The second digit to the right is the hundredths place, because it represents the represents the proportion out of 100 equal parts of a whole. The third digit to the right of the decimal is thousandths because it represents the proportion of of 1000 parts of a whole.

### Step 3

Write out a number's expanded form by writing each digit and explaining its place value in mathematical terms. For example, the number 3,047 is, 3 x 1,000 + 0 x 100 + 4 x 10 + 7 x 1 in its expanded form.

### Step 4

Do the math to check your work. In this example, 3 x 1,000 = 3,000; 0 x 100 =0; 4 x 10 = 40; and 7 x 1 = 7. Your expanded format is correct because 3,000+0+40+7=3,047, which is the standard form of the number.

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