Convert Decimal 0.505 to Simplified Fraction Form

Question

Convert 0.505 into a fraction.

Video Solution

Step-by-Step Solution

To convert the decimal 0.505 into a fraction, follow these steps:

  • Step 1: Recognize that the decimal 0.505 can be expressed as 5051000 \frac{505}{1000} . This is because there are three digits after the decimal point, so we use 1000 as the denominator.
  • Step 2: Check if the fraction can be simplified. The greatest common divisor (GCD) of 505 and 1000 is 5. Therefore, we divide both the numerator and the denominator by their GCD to simplify the fraction.
  • Step 3: Simplifying 5051000\frac{505}{1000}, we divide both the numerator and the denominator by 5:
    505÷51000÷5=101200 \frac{505 \div 5}{1000 \div 5} = \frac{101}{200}
  • Step 4: The fraction 101200\frac{101}{200} is in its simplest form, as 101 is a prime number, and no further simplification is possible.

Therefore, the decimal 0.505 is equal to the fraction 5051000 \frac{505}{1000} , which simplifies to 101200 \frac{101}{200} .

Given the multiple-choice options, the correct answer based on the problem's form is:

5051000 \frac{505}{1000}

Answer

5051000 \frac{505}{1000}