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What is a Terminating Decimal?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
A terminating decimal is a decimal number that has a finite number of digits after the decimal point. This means the decimal expansion ends, it doesn't go on forever. You can write it completely without needing '...' at the end.
Simple Example
Quick Example
Imagine you bought a samosa for ₹15.50. This is a terminating decimal because the price ends after two digits (50) after the decimal point. You don't say ₹15.505050... right? It's a clear, exact value.
Worked Example
Step-by-Step
Let's check if 3/4 is a terminating decimal.
1. Divide the numerator (3) by the denominator (4).
2. Set up the long division: 3 divided by 4.
3. Since 3 is smaller than 4, put a 0 in the quotient and add a decimal point, then add a zero to 3, making it 30.
4. Now, divide 30 by 4. 4 times 7 is 28. Write 7 after the decimal point in the quotient.
5. Subtract 28 from 30, which leaves 2.
6. Add another zero to 2, making it 20.
7. Divide 20 by 4. 4 times 5 is 20. Write 5 in the quotient.
8. Subtract 20 from 20, which leaves 0. The remainder is 0, so the division ends.
Answer: 3/4 = 0.75. Since it has a finite number of digits after the decimal point (7 and 5), it is a terminating decimal.
Why It Matters
Understanding terminating decimals is crucial in fields like Data Science and Computer Science, where exact measurements and calculations are needed. Engineers use them for precise designs, and economists rely on them for accurate financial reporting, making these concepts fundamental for many exciting careers.
Common Mistakes
MISTAKE: Thinking all fractions result in terminating decimals. | CORRECTION: Only fractions whose denominators (in simplest form) have prime factors only of 2 or 5 (or both) will terminate.
MISTAKE: Confusing terminating decimals with repeating decimals. | CORRECTION: Terminating decimals end, while repeating decimals have a pattern that goes on forever (e.g., 0.333... or 0.121212...).
MISTAKE: Not simplifying the fraction before checking the denominator. | CORRECTION: Always simplify the fraction to its lowest terms first. For example, 6/8 simplifies to 3/4, then check the denominator 4.
Practice Questions
Try It Yourself
QUESTION: Is 1/2 a terminating decimal? | ANSWER: Yes, 1/2 = 0.5, which ends.
QUESTION: Convert 7/8 to a decimal and state if it's terminating. | ANSWER: 7/8 = 0.875. Yes, it is a terminating decimal.
QUESTION: Which of these fractions will result in a terminating decimal: 1/3, 3/5, 5/6? Explain why. | ANSWER: 3/5. Because 3/5 = 0.6, which ends. 1/3 = 0.333... (repeating) and 5/6 = 0.8333... (repeating), as their denominators (3 and 6) have prime factors other than just 2s and 5s.
MCQ
Quick Quiz
Which of the following is a terminating decimal?
0.111...
0.25
0.333...
0.142857142857...
The Correct Answer Is:
B
Option B, 0.25, is a terminating decimal because it ends after two digits. Options A, C, and D are repeating decimals as their digits continue infinitely in a pattern.
Real World Connection
In the Real World
When you check your mobile data usage, it might show 1.75 GB remaining. This is a terminating decimal, giving you an exact, finite value. Similarly, prices of groceries, petrol, or even your cricket team's run rate are often expressed as terminating decimals for clarity and precision.
Key Vocabulary
Key Terms
DECIMAL: A number that includes a whole number part and a fractional part, separated by a decimal point. | FINITE: Having an end or a limit. | NUMERATOR: The top number in a fraction. | DENOMINATOR: The bottom number in a fraction. | PRIME FACTORS: The prime numbers that multiply together to make a number.
What's Next
What to Learn Next
Great job understanding terminating decimals! Next, you should explore 'Non-Terminating Repeating Decimals'. This will help you understand the other type of decimal expansion and how it's different from what you just learned.
