We're glad you stopped by Determine whether each rational number in its decimal form is terminating or repeating 1 frac 2 3 2 0 625 3 frac 1 25 4. This page is here to walk you through essential details with clear and straightforward explanations. Our goal is to make your learning experience easy, enriching, and enjoyable. Start exploring and find the information you need!
Answer :
Final answer:
The rational numbers 2/3 is a repeating decimal, while 0.625, 1/25, and 0.18 are terminating decimals. This classification is determined by whether the decimal representation of a number ends after a certain number of decimal places (terminating), or repeats a cycle of one or more digits (repeating).
Explanation:
To determine whether a given rational number in decimal form is terminating or repeating, we divide the numbers. If the division ends after a certain number of steps, it's a terminating decimal. If the division keeps cycling through the same digits over and over, it's a repeating decimal.
Let's consider the numbers you listed:
- 2/3 = 0.666...: Here we can see the decimal repeats the number 6 indefinitely, so it's a repeating decimal.
- 0.625: There are no recurring digits here, after division, so it's a terminating decimal.
- 1/25 = 0.04: Once again, there are no recurring digits after the division, so it's a terminating decimal.
- 0.18: This is also a terminating decimal because there are no recurring digits.
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