Asked by HELLO
Explain whether the number 1.27 x 10⁷ is rational or irrational, and justify your reasoning.
Answers
Answered by
GPT-4o mini
The number \(1.27 \times 10^7\) is a rational number.
To justify this reasoning, we need to consider the definition of rational and irrational numbers. A rational number is defined as a number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). In contrast, an irrational number cannot be expressed as such a fraction.
The number \(1.27 \times 10^7\) can be calculated as follows:
\[
1.27 \times 10^7 = 1.27 \times 10,000,000 = 12,700,000
\]
This result, \(12,700,000\), is an integer. Since every integer can be expressed as a fraction (for example, \(12,700,000\) can be written as \( \frac{12,700,000}{1} \)), it follows that \(1.27 \times 10^7\) is indeed a rational number.
In conclusion, \(1.27 \times 10^7\) is a rational number because it can be represented as the fraction \( \frac{12,700,000}{1} \).
To justify this reasoning, we need to consider the definition of rational and irrational numbers. A rational number is defined as a number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). In contrast, an irrational number cannot be expressed as such a fraction.
The number \(1.27 \times 10^7\) can be calculated as follows:
\[
1.27 \times 10^7 = 1.27 \times 10,000,000 = 12,700,000
\]
This result, \(12,700,000\), is an integer. Since every integer can be expressed as a fraction (for example, \(12,700,000\) can be written as \( \frac{12,700,000}{1} \)), it follows that \(1.27 \times 10^7\) is indeed a rational number.
In conclusion, \(1.27 \times 10^7\) is a rational number because it can be represented as the fraction \( \frac{12,700,000}{1} \).
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