To convert the decimal 0.643 to a fraction, follow these steps:
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Identify the decimal place: The decimal 0.643 has three digits after the decimal point.
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Convert to a fraction: Write the decimal as a fraction with the decimal's digits as the numerator and \(10^3\) (or 1000) as the denominator because there are three decimal places.
\[ 0.643 = \frac{643}{1000} \]
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Simplify the fraction: Now, we need to check if the fraction can be simplified. We can do this by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 643 and 1000 is 1 since 643 is a prime number and does not divide evenly into 1000.
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Final Simplified Fraction: Since the GCD is 1, the fraction \(\frac{643}{1000}\) is already in its simplest form.
Thus, the decimal 0.643 converted to a fraction in simplest form is:
\[ \frac{643}{1000} \]
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