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11 Here is a decimal:
5.020020002000020000020000002 dots
Arun says:
There is a regular pattern: one zero, then two zeros, then three zeros, and so on. This is a rational number.
a Is Arun correct? Give a reason for your answer.
b Compare your answer with a partner's. Do you agree? If not, who is correct?

$11$ Here is a decimal: $5.020020002000020000020000002 \ldots$ $\newline$ Arun says: $\newline$ There is a regular pattern: one zero, then two zeros, then three zeros, and so on. This is a rational number. $\newline$ a Is Arun correct? Give a reason for your answer. $\newline$ b Compare your answer with a partner's. Do you agree? If not, who is correct?

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Find probabilities using the binomial distribution

Full solution

Q.

11

Here is a decimal:

5.020020002000020000020000002 \ldots

\newline

Arun says:

\newline

There is a regular pattern: one zero, then two zeros, then three zeros, and so on. This is a rational number.

\newline

a Is Arun correct? Give a reason for your answer.

\newline

b Compare your answer with a partner's. Do you agree? If not, who is correct?

Question Prompt: question_prompt: Is Arun's observation about the decimal $5.020020002000020000020000002$ correct, and is it a rational number?
Pattern Observation: Arun observes a pattern in the decimal: one $0$ , then two $0$ s, then three $0$ s, and so on. To determine if this is a rational number, we need to check if the pattern repeats indefinitely.
Rational Number Definition: A rational number can be expressed as a fraction where both the numerator and the denominator are integers. Since the pattern in the decimal repeats, it can be written as a fraction.
Infinite Series Representation: The decimal can be expressed as a series where each term adds more zeros before the digit $2$ . This series is infinite and follows a clear pattern, which means it can be represented as a repeating decimal.
Fraction Conversion: Since the decimal is repeating, it can be expressed as a fraction. Therefore, Arun is correct; the number is rational.
Comparison and Discussion: Compare the answer with a partner's. If there's a disagreement, discuss to find out who has the correct understanding of rational numbers.

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