Question

Convert the decimal below to a fraction in simplest form.
0.437

Answer 1

To convert the decimal \(0.437\) to a fraction, we follow these steps:

1. 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:

\[
0.437 = \frac{437}{1000}
\]

2. 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.

3. 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.

4. The denominator \(1000\) can be factored as follows:

\[
1000 = 10^3 = (2 \cdot 5)^3 = 2^3 \cdot 5^3
\]

5. 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 \(1\).

6. 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:

\[
\frac{437}{1000}
\]