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Classify the decimal forms of [tex]\frac{1}{3}[/tex] and 210 as repeating or terminating.

Options:
1. [tex]\frac{1}{3}[/tex] - Terminating, 210 - Terminating
2. [tex]\frac{1}{3}[/tex] - Repeating, 210 - Terminating
3. [tex]\frac{1}{3}[/tex] - Terminating, 210 - Repeating
4. [tex]\frac{1}{3}[/tex] - Repeating, 210 - Repeating

Correct Option: Option 2

Answer :

Final answer:

1/3 produces a decimal form of 0.333 which repeats indefinitely, making it a repeating decimal. Whole number 210's decimal form (210.0) ends and doesn't repeat, classifying it as a terminating decimal. Therefore, option 2 (1/3 - Repeating, 210 - Terminating) is correct.

Explanation:

In Mathematics, a decimal is defined as terminating if it ends or 'terminates'. In contrast, a decimal is considered repeating if a digit or a set of digits repeat indefinitely. Now, let's classify the given numbers.

Let's first calculate the decimal equivalent of 1/3. If you perform the division, you will notice that it results in a decimal form of 0.333... This pattern of 3 continues without an end, hence, 1/3 is a repeating decimal.

Now, let's consider 210. As it is a whole number, its decimal representation (210.0) does not continue indefinitely or 'repeat'. Thus, 210 is a terminating decimal value.

So, comparing with your provided options, the correct answer is: Option 2: 1/3 - Repeating, 210 - Terminating.

Learn more about Decimal Classification here:

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