Math Help: Decimals and Place Values

The Place Value and Decimal Systems

Place Values for Whole Numbers

Every whole number (except the number one) can be expressed as the sum of the smaller whole numbers that comprise it. For example, the number 325 contains three hundreds, two tens and five ones, so we could represent it in any of the following ways:

300 + 20 + 5

(3 x 100) + (2 x 10) + (5 x 1)

100 + 100 + 100 + 10 + 10 + 1 + 1 + 1 + 1 + 1

Instead of writing all this out, we use the place value system. In this system, the digit to the far right (like the five in 325) represents the quantity of 'ones' in the number, so it's called the ones place. The middle digit (like the two in 325) is in the tens place, and it represents the number of 'tens' in the number. The digit on the left (like the three in 325) is in the hundreds place, and it tells you how many 'hundreds' the number has.

The place value of each digit in a number is ten times the place value of the digit to its right. For instance, if a number has a fourth digit to the left of the hundreds place, this is called the thousands place because 100 x 10 = 1,000. Likewise, each digit's place value is 1/10 the place value of the digit to its left. For example, the place value of the tens place is 1/10 the place value of the hundreds place because 10/100 = 1/10.

Decimal Place Values

Decimals are digits placed to the right of the decimal point, and they represent fractions of one. With decimals, the space between two whole numbers can be divided into tenths (1/10), hundredths (1/100), thousandths (1/1,000) or even smaller amounts, depending on how precise your measurement is. Notice there's no such thing as a 'oneths' decimal place because 1/1 = 1, and whole numbers are written on the left side of the decimal point.

In a decimal like 1.234, the two is in the tenths place, the three is in the hundredths place and the four is in the thousandths place. As with whole number place values, each decimal place value is 1/10 the value of the place to its left (for example, 1/1,000 is 1/10 of 1/100) and ten times the place value of the digit to its right (for instance, 1/10 = 1/100 x 10).