Decimal fractions have values less than 1. A number, such as 2.38, which has a decimal fraction as well as a whole number portion, is sometimes referred to as a decimal mixed number. However, the term "decimal" can also be used to refer to both decimal fractions or decimal mixed numbers.
Converting a decimal to a fraction involves understanding place value. Notice that in the examples above, the number of 0s in the denominator is equal to the number of digits after the decimal point. 0.1 has only 1 digit after the decimal point, 1, and its fraction form is 1/10. It is possible to convert decimals to fractions by remembering that the number of 0s attached to the 1 in the denominator is equal to the number of digits after the decimal point. However, the reason that this works is because of the nature of the decimal numeral system, which is the most widely used numeral system. Thus, understanding it as it relates to place value will give you a foundation for working with other mathematical concepts.
How to write decimal fractions
The numerator of a decimal fraction is made up of the non-zero digits in the decimal. The denominator is a power of 10 that is based on the position of the last non-zero digit in the decimal. For example, in 0.625, the place value of the "5" (thousandths) determines the denominator. Thus, for 0.625, the non-zero digits are 6, 2, and 5, which are written over the place value, 1000:
To see why this works, we could break the number up into the value of each of its digits:
To add fractions, they need to share the same denominator, so convert each digit to equivalent fractions. Since all the denominators are powers of 10, the least common denominator is the largest power of 10, or 1000 in this case:
It can be helpful to write out each digit's value until the student is comfortable with the concept of place value, after which they can just immediately write all the digits in the numerator over the appropriate power of 10 in the denominator.
Below is a place value chart ranging from the ones to the ten-thousandths. The place values continue in either direction, but for the purpose of decimal fractions, only this range is shown as an example.