TERMINATING DECIMAL
Definition Of Terminating Decimal
The word "terminate" means "end".
A decimal that ends is a terminating decimal.
In other words, a terminating decimal doesn't keep going. A terminating decimal will have a finite number of digits after the decimal point.
Examples of Terminating Decimal
In the examples listed above, we have a few fractions expressed as decimals. Notice that these decimals have a FINITE NUMBER OF DIGITS after the decimal point. So, they are terminating decimals.
However, there are situations when the digits after the decimal point DOES NOT END or they go on forever. They are called non-terminating decimals.
Video Examples: Terminating and Repeating Decimals
Solved Example on Terminating Decimal
Ques: Which is a terminating decimal between 8/11 and 11/8?
Solution:
Let's first convert the fractions into decimals by dividing the numerator by the denominator.
Quick Summary
- Terminating decimals have a finite number of digits after the decimal point.
- They represent fractions that can be expressed with a denominator that is a power of 10 (e.g., 10, 100, 1000).
⚠️ Common Mistakes
- Confusing terminating decimals with repeating decimals.
- Assuming all fractions can be represented as terminating decimals.
🌍 Real-World Uses
- Calculating the final cost of an item after sales tax, where the tax is expressed as a terminating decimal (e.g., 6.25% tax).
- Measuring ingredients in cooking with digital scales that display weights as terminating decimals (e.g., 2.5 grams of salt).
- Representing currency amounts (e.g., $19.99), where the decimal portion represents cents as a terminating decimal.
📋 Standards Alignment
CCSS.MATH.NS.7.3CCSS.MATH.NS.8.2
🔗 Related Links
🍎 Teacher Insights
Use visual aids like number lines and fraction strips to demonstrate terminating decimals. Emphasize the connection between fractions and decimal representation.🎓 Prerequisites
- Fractions
- Division
- Decimal Representation
Check Your Knowledge
Q1: Which of the following is a terminating decimal?
Frequently Asked Questions
Q: How can I tell if a fraction will result in a terminating decimal?
A: If the simplified fraction's denominator only has prime factors of 2 and/or 5, it will result in a terminating decimal.