Terminating decimals, also known as finite decimals, are decimals that end after a finite number of digits. They are characterized by having a denominator that is a factor of 10, such as 10, 100, or 1000. Terminating decimals are often contrasted with repeating decimals, which have a denominator that is not a factor of 10. Unlike repeating decimals, terminating decimals can be represented as fractions with integer denominators.
What is a Terminating Decimal?
A terminating decimal is a decimal that ends after a finite number of digits. This is because a terminating decimal represents a rational number, which is a number that can be expressed as a fraction of two integers.
For example, the decimal 0.5 is a terminating decimal because it can be written as the fraction 1/2. The decimal 0.25 is also a terminating decimal because it can be written as the fraction 1/4.
Here are some of the properties of terminating decimals:
- They always end in a zero.
- They can be written as a fraction of two integers.
- They are rational numbers.
Here is a table that summarizes the properties of terminating decimals:
| Property | Description |
|---|---|
| Ends in a zero | The last digit of a terminating decimal is always 0. |
| Can be written as a fraction of two integers | Terminating decimals can be written as a fraction of two integers, where the denominator is a power of 10. |
| Are rational numbers | Terminating decimals are rational numbers, which means they can be expressed as a fraction of two integers. |
Question 1:
What is the definition of a terminating decimal?
Answer:
A terminating decimal is a decimal number that has a finite number of digits after the decimal point. The number of digits after the decimal point is called the period.
Question 2:
How do you know if a decimal is terminating?
Answer:
A decimal is terminating if the denominator of the fraction that represents the decimal is a power of 10.
Question 3:
What is the significance of terminating decimals?
Answer:
Terminating decimals are important because they can be represented as fractions with a finite number of digits in the denominator. This makes them easier to work with than non-terminating decimals.
Well, there you have it, folks! You now know everything you ever wanted to know about terminating decimals – or at least, enough to impress your friends at your next math party. (Don’t worry, we won’t tell them you learned it from us.) Thanks for reading, and be sure to check back later for more math mysteries unraveled! Until next time, keep your calculators close and your numbers straight.