In this lesson, you will learn about the definition of a terminating decimal and walk through several examples. At the end, you’ll get to test your new knowledge with a quiz.
What Is A Terminating Decimal?
In case you forgot, a decimal is a number with a decimal point. There are usually numbers to the left and numbers to the right of that decimal point. For example, 0.5 and 12.56 are both decimals. Decimals allow us to represent partial amounts of a whole, just like fractions. As a matter of fact, many decimals and fractions are interchangeable so either form can be used.
Today, we are going to focus on one type of decimal, the terminating decimal. What does the word terminate mean? When I hear this word, I always think of the 1984 film, The Terminator starring Arnold Schwarzenegger, and the terminator saying ‘Hasta la vista baby’ right before he defeated the machine. So, from this we realize that terminate means to bring to an end. In terms of a decimal, it is a decimal that has an end.
How To Recognize A Terminating Decimal
A terminating decimal has a set or finite amount of numbers after the decimal point. For example, you go to the store and buy one t-shirt for $14.99, a pair of shorts for $21.75, and a pair of socks for $3.00. These are all terminating decimals because they end. These examples only have two digits after the decimal point. You go out to lunch and buy a sandwich, chips, and a drink for $5.99. This is another example of a terminating decimal. Generally, all of the money you spend and earn is recorded as a terminating decimal.
Of course, terminating decimals can be longer as well. Let’s look at the fraction 1/8. In decimal form it is 0.125, which is a terminating decimal. The fraction 29/200 is 0.145 as a decimal, which is another terminating decimal. 51.202211 is also a terminating decimal because the number ends after the last 1. Terminating decimals can also repeat, but they must still have an end, such as 0.4545.
Most statistics kept for athletes are terminating decimals. In 1951, playing for the Yankees, Mickey Mantle had a batting average of 0.267. In the 2015 Super Bowl, the Patriots averaged 6.3 yards per pass, while the Seahawks averaged 9.8 yards per pass. Both of these are terminating decimals.
Non Terminating Decimals
In comparison, it is fair to briefly review non terminating decimals. Just from the name we can see that these decimals are the opposite. Non terminating decimals go to, as Buzz Lightyear said, ‘infinity and beyond.’
A common non terminating decimal is the decimal form of 1/3. Performing the long division we arrive at 0.333333333… and so on. This decimal goes on forever with the number 3 repeating over and over again. Its cousin 2/3, is also non terminating as 0.666666666… and so on, because the 6 repeats and goes on forever.
We can represent a non terminating decimal with an ellipsis (…). These three dots indicate that the pattern or numbers continue on forever.
So we have learned that a terminating decimal is a decimal that has an end or a finite number of digits after the decimal point. A terminating decimal may have one digit after the decimal point, may have a repeated pattern, or may have many digits after the decimal point. As long as the digits stop and have an ending point, we have a terminating decimal.