The decimal equivalent 3/5 is a repeating decimal true or false?
The Correct Answer and Explanation is:
The statement that the decimal equivalent of 3/5 is a repeating decimal is false.
Explanation:
To understand why 3/5 is not a repeating decimal, let’s first convert 3/5 into its decimal form through long division:
- Dividing 3 by 5:
- First, we perform the division of 3 by 5. Since 5 doesn’t go into 3, we place a 0 before the decimal point.
- Now, we add a decimal point and bring down a 0 (making the number 30).
- 5 goes into 30 exactly 6 times (5 × 6 = 30), leaving no remainder.
- Thus, the decimal equivalent of 3/5 is 0.6.
Since the division process results in a finite decimal (0.6), it is not a repeating decimal. Repeating decimals occur when the division results in an infinitely repeating sequence of digits after the decimal point. For example, 1/3 equals 0.333…, where the digit “3” repeats forever.
Key Points:
- Repeating Decimals: A repeating decimal is one where a sequence of digits after the decimal point repeats infinitely. For instance, the fraction 1/3 is written as 0.333…, with the “3” repeating indefinitely.
- Terminating Decimals: A terminating decimal is a decimal that has a finite number of digits after the decimal point. In the case of 3/5, the decimal is 0.6, which has only one digit after the decimal point. It does not repeat, hence it is a terminating decimal.
General Rule:
- Fractions with denominators that are factors of 10 (such as 2, 5, or 10) will have terminating decimal expansions. This is because powers of 10 are divisible by these numbers, and the division results in a finite number of digits.
- Fractions with other denominators, particularly those that have prime factors other than 2 or 5, tend to produce repeating decimals. For example, 1/7 results in 0.142857…, where the “142857” repeats forever.
Thus, 3/5 is a terminating decimal, not a repeating decimal.