A “decimal fraction” is part of a whole, like a fraction, but it uses a decimal point and place value to show amounts. It can be more or less than a whole. The Common Core State Standards require fourth grade students to understand two places to the right of the decimal point, the tenths place and the hundredths place. An example would be 0.38 or thirty-eight hundredths. To help students understand decimal fraction concepts, we use place value charts and disks, draw pictures, and work abstractly.
As in the fraction unit, the flat is considered 1, or 1 whole, a long is a tenth because 10 longs make a whole, and a small cube is a hundredth because 100 cubes make a whole. As we work, I encourage students to realize that ten hundredths make a tenth.
We practice decimal fraction concepts abstractly with these kinds of exercises:
“Write twenty-four hundredths as a decimal fraction.”
“Write twelve and four tenths as a decimal fraction.”
“Write this decimal fraction (0.47) in word form.”
“Write this decimal fraction (3 + 0.8 + 0.02) in standard form.”
“Write a decimal fraction that has four tenths, two wholes, and six hundredths.”