Terminating Decimal

Definition

A terminating decimal is a decimal number that can be expressed as a fraction with a finite number of digits in the denominator. In other words, the decimal representation of the number eventually stops or terminates, rather than repeating infinitely.

5 Must Know Facts For Your Next Test

1. Terminating decimals can always be expressed as a fraction with a denominator that is a power of 10.
2. The decimal representation of a terminating decimal will eventually stop, meaning it has a finite number of digits after the decimal point.
3. Any fraction with a denominator that is a product of 2s and 5s will result in a terminating decimal.
4. Terminating decimals are a subset of rational numbers, as they can be expressed as a fraction.
5. The decimal representation of a terminating decimal can be converted to a fraction by placing the digits after the decimal point in the numerator and the appropriate power of 10 in the denominator.

Review Questions

• Explain the relationship between terminating decimals and fractions.
  • Terminating decimals are a type of rational number that can be expressed as a fraction with a finite number of digits in the denominator. This means that the decimal representation of a terminating decimal will eventually stop, rather than repeating infinitely. Any fraction with a denominator that is a product of 2s and 5s will result in a terminating decimal, as the denominator can be expressed as a power of 10. Conversely, a terminating decimal can always be converted to a fraction by placing the digits after the decimal point in the numerator and the appropriate power of 10 in the denominator.
• Describe the differences between terminating decimals and repeating decimals.
  • The key difference between terminating decimals and repeating decimals is the nature of their decimal representation. Terminating decimals have a decimal representation that eventually stops, with a finite number of digits after the decimal point. In contrast, repeating decimals have a decimal representation that continues to repeat a pattern of digits indefinitely. Terminating decimals can always be expressed as a fraction with a denominator that is a power of 10, while repeating decimals cannot be expressed as a fraction with a finite denominator.
• Analyze the significance of terminating decimals in the context of rational numbers and decimal representations.
  • Terminating decimals are significant because they represent a subset of rational numbers that can be expressed in a particularly simple and straightforward way. The fact that terminating decimals can always be written as a fraction with a denominator that is a power of 10 makes them easier to work with and understand compared to repeating decimals. Additionally, the finite nature of their decimal representation means that terminating decimals can be more precisely represented and calculated than repeating decimals. This makes terminating decimals an important concept in the study of decimal representations and the properties of rational numbers.

Related terms

Repeating Decimal:

A repeating decimal is a decimal number where the digits after the decimal point repeat in a pattern that continues indefinitely.

Fraction:

A fraction is a numerical quantity that is expressed as a part of a whole, represented by a numerator and a denominator.

Rational Number: A rational number is a number that can be expressed as a fraction, where the numerator and denominator are both integers, and the denominator is not zero.