Decimals

What's the point (of the decimal point)?

The structure of our number system is based upon a simple pattern of tens in which each place is ten times the value of the place to its right. This is known as a ten-to-one place value relationship. A decimal point separates the whole number places from the places less than one. Place values extend infinitely in two directions from a decimal point.

3 3 3 . 3 3 HTU . t h

The 3 in the hundreds place (H) has a value 10 times greater than the 3 in the tens place (T) which has a value 10 times greater than the 3 in the units (ones) place (U). The same pattern holds true for the fractional part of the numbers to the right of the decimal point: the 3 in the units place has a value 10 times greater than the 3 in the tenths place (t), and the 3 in the tenths place has a value 10 times greater than the 3 in the hundredths place (h).

Decimals are often modeled using squares such as shown below. The large square in its entirety represents 1 whole. The second square is divided into ten equal parts, or tenths. The next square shows each of those tenths divided into ten equal parts, for a total of 100 parts, or hundredths. In the square on the right, each of the hundredths has been divided into ten equal parts, for a total of 1,000 parts in the whole, or thousandths.

Decimals can also be shown on a number line model. The number lines below depict the fractional (decimal) numbers between zero and one. The first number line is divided into ten parts (tenths), and the second number line is divided into one hundred parts (hundredths). The number lines also show why the number 0.1 (one tenth) is equal to 0.10 (ten hundredths).

To read decimal numbers:

• read the whole number to the left of the decimal point;

• read the decimal point as “and”;

• read the digits to the right of the decimal point just as you would read a whole number;

• and say the name of the place value of the digit in the smallest place.

For example: 14.34 is read as "fourteen and thirty-four hundredths"

To investigate decimals on a number line, click on the images below that link to a page with a "zoomable" number line. Investigate smaller and smaller decimal numbers that are located in between other numbers on the number line.