How to Express 0.3825 as a Fraction?

Find what is the decimal 0.3825 as a fraction in a straightforward process. Below, is the step-by-step method for simplifying the fraction.

Step 1: Write the Decimal 0.3825 as a Fraction

At First, observe that there are four digits following the decimal point in 0.3825, so we can convert it to a fraction by writing it as: This implies that the denominator should be 10⁴=10000. Thus:

0.3825=\frac{3825}{10000}​

Step 2: Simplify the Fraction

The next step is to simplify \frac{3825}{10000}​​. To do this, find the greatest common divisor (GCD) of 3825 and 10000.

1. Prime Factorization :
   • 3825 = 3²×5²×17
   • 10000 = 2⁴×5⁴
2. Common Factors: 3825 and 10000 have a common factor which is 5² = 25.
3. Simplify: Divide both the numerator and denominator by 25: \frac{3825}{10000}​=\frac{3825÷25}{10000÷25}​=\frac{153}{400}​

So, the simplified fraction is: \frac{153}{400}​​

Step 3: Explore All Possible Combinations

While \frac{153}{400} is the simplest form, other equivalent fractions can be derived by multiplying the numerator and denominator by the same number. For example:

1. Multiply by 2:\frac{153 \times 2}{400 \times 2} = \frac{306}{800}​
2. Multiply by 3:\frac{153 \times 3}{400 \times 3} = \frac{459}{1200}​​
3. Multiply by 4:\frac{153 \times 4}{400 \times 4} = \frac{612}{1600}​​

This process can continue indefinitely, but \frac{153}{400} remains the simplest form. Check the decimal to fraction tool if you want to find the answer in one click.