Terminating decimals are numbers that have a finite number of digits after the decimal point. They are closely related to rational numbers, which can be expressed as the ratio of two integers, and to repeating decimals, which have a repeating pattern of digits after the decimal point. Terminating decimals can also be classified as either positive or negative, depending on the sign of the number.
Terminating Decimals
Terminating decimals are a type of decimal that has a finite number of digits. This means that the decimal will eventually end, and there will be no more non-zero digits after the last digit. Terminating decimals can be represented in either fractional or decimal form.
Fractional Form
In fractional form, terminating decimals are written as a fraction with a denominator that is a power of 10. For example, the decimal 0.5 can be written as the fraction 5/10. The denominator, 10, indicates that there is one non-zero digit after the decimal point.
Decimal Form
In decimal form, terminating decimals are written as a number with a decimal point and a finite number of digits after the decimal point. For example, the decimal 0.5 can be written as 0.5.
Properties of Terminating Decimals
Terminating decimals have the following properties:
- They can be represented as a fraction with a denominator that is a power of 10.
- They have a finite number of digits after the decimal point.
- They can be converted to fractions by multiplying the decimal by a power of 10.
Converting Terminating Decimals to Fractions
To convert a terminating decimal to a fraction, follow these steps:
- Count the number of digits after the decimal point.
- Multiply the decimal by a power of 10 that has the same number of zeros as the number of digits after the decimal point.
- Simplify the fraction, if possible.
For example, to convert the decimal 0.5 to a fraction, follow these steps:
- Count the number of digits after the decimal point. There is one digit after the decimal point.
- Multiply the decimal by a power of 10 that has the same number of zeros as the number of digits after the decimal point. 0.5 * 10^1 = 5
- Simplify the fraction. 5/10 = 1/2
Table of Terminating Decimals
The following table shows some examples of terminating decimals and their fractional equivalents:
| Decimal | Fraction |
|---|---|
| 0.5 | 1/2 |
| 0.25 | 1/4 |
| 0.125 | 1/8 |
| 0.0625 | 1/16 |
| 0.03125 | 1/32 |
Question 1:
What is the definition of a terminating decimal?
Answer:
A terminating decimal is a number that can be expressed as a finite number of digits after the decimal point.
Question 2:
How are terminating decimals different from non-terminating decimals?
Answer:
Terminating decimals have a fixed number of digits after the decimal point and eventually end, while non-terminating decimals continue indefinitely without repeating.
Question 3:
Why are terminating decimals considered rational numbers?
Answer:
Terminating decimals represent rational numbers because they can be expressed as a fraction of two integers with a non-zero denominator.
Thanks for reading, folks! I hope this little dive into terminating decimals has been helpful. Remember, they’re the ones that eventually end, like a racecar crossing the finish line. If you’ve got any more decimals that you’re curious about, feel free to drop back by. I’m always happy to chat about the fascinating world of numbers. Until next time, keep those calculators humming!