Step-by-Step Solution for Converting 0.2 to a Fraction

Step 1: Understand the Number

The number 0.2 is a decimal, which can be broken into two parts:

• The whole number part is: 0.
• The decimal part is: 0.2.

We aim to convert the entire number into a fraction.

Step 2: Isolate the Decimal Part (0.2)

Focus on the decimal part (0.2) and represent it as a fraction.

Step 2.1: Write 0.2 as \( \frac20100 \)

The decimal 0.2 can be read as "20 hundredths." Mathematically, this is:

\[ 0.2 = \frac20100 \]

Step 2.2: Simplify the Fraction

Now simplify \( \frac20100 \) by finding the greatest common divisor (GCD) of 20 and 100.

• The GCD of 20 and 100 is: 20.
• Therefore, the simplified fraction is:

\[ \frac15 \]

Step 3: Combine the Whole Number and Fraction

The original number 0.2 is the sum of the whole number 0 and the fraction \( \frac15 \).

Combine these as a mixed number:

\[ 0.2 = 0 + \frac15 = \frac1/5 \]

Step 4: Verify the Answer

To verify, divide \( \frac1/5 \):

\[ \frac1/5 = 0.2 \]

Thus, the fraction is correct.

Final Answer

The decimal 0.2 as a fraction is:

\[ \frac1/5 \]

If expressed as a mixed number:

\[ 1/5 \]