To convert the decimal \(0.437\) to a fraction, we follow these steps:
- Write the decimal as a fraction with the decimal part in the numerator and a power of 10 in the denominator. Since \(0.437\) has three decimal places, we can write it as:
\[ 0.437 = \frac{437}{1000} \]
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Next, we need to simplify the fraction \(\frac{437}{1000}\) if possible. To do this, we need to see if the numerator and the denominator share any common factors.
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The number \(437\) is checked for prime factors. The prime factorization of \(437\) reveals that it is not divisible by \(2\), \(3\), \(5\), or \(7\). In fact, \(437\) is a prime number.
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The denominator \(1000\) can be factored as follows:
\[ 1000 = 10^3 = (2 \cdot 5)^3 = 2^3 \cdot 5^3 \]
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Since the number \(437\) has no factors in common with \(1000\) (as \(437\) is prime), the greatest common divisor (GCD) of \(437\) and \(1000\) is \(1\).
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Therefore, we cannot simplify the fraction further, and it is already in its simplest form.
Thus, the decimal \(0.437\) as a fraction in simplest form is:
\[ \frac{437}{1000} \]