3.1875 as a fraction

Steps to Solve

1. Separate Whole and Decimal Parts

Identify the whole number part and the decimal part of the decimal number 3.1875.

The whole number part is $3$, and the decimal part is $0.1875$.

2. Convert Decimal to Fraction

Convert the decimal $0.1875$ into a fraction. First, recognize that $0.1875$ can be expressed as:

$$ 0.1875 = \frac{1875}{10000} $$

This is because there are four decimal places.

3. Simplify the Fraction

Next, simplify the fraction $\frac{1875}{10000}$ by finding the greatest common divisor (GCD) of the numerator and denominator.

The GCD of $1875$ and $10000$ is $125$.

Thus, we divide both the numerator and the denominator by $125$:

$$ \frac{1875 \div 125}{10000 \div 125} = \frac{15}{80} $$

4. Combine Whole Number and Fraction

Now, combine the whole number part with the simplified fraction:

$$ 3 + \frac{15}{80} $$

We can convert this to an improper fraction:

$$ \frac{3 \cdot 80 + 15}{80} = \frac{240 + 15}{80} = \frac{255}{80} $$

5. Final Simplification (if needed)

Check if the final fraction can be simplified. The GCD of $255$ and $80$ is $1$, thus:

The fraction $\frac{255}{80}$ is already in its simplest form.