Step-by-Step Solution for Converting 0.52 to a Fraction

Step 1: Understand the Number

The number 0.52 is a decimal, which can be broken into two parts:

• The whole number part is: 0.
• The decimal part is: 0.52.

We aim to convert the entire number into a fraction.

Step 2: Isolate the Decimal Part (0.52)

Focus on the decimal part (0.52) and represent it as a fraction.

Step 2.1: Write 0.52 as \( \frac52100 \)

The decimal 0.52 can be read as "52 hundredths." Mathematically, this is:

\[ 0.52 = \frac52100 \]

Step 2.2: Simplify the Fraction

Now simplify \( \frac52100 \) by finding the greatest common divisor (GCD) of 52 and 100.

• The GCD of 52 and 100 is: 4.
• Therefore, the simplified fraction is:

\[ \frac1325 \]

Step 3: Combine the Whole Number and Fraction

The original number 0.52 is the sum of the whole number 0 and the fraction \( \frac1325 \).

Combine these as a mixed number:

\[ 0.52 = 0 + \frac1325 = \frac13/25 \]

Step 4: Verify the Answer

To verify, divide \( \frac13/25 \):

\[ \frac13/25 = 0.52 \]

Thus, the fraction is correct.

Final Answer

The decimal 0.52 as a fraction is:

\[ \frac13/25 \]

If expressed as a mixed number:

\[ 13/25 \]