Step-by-Step Solution for Converting 1.09 to a Fraction

Step 1: Understand the Number

The number 1.09 is a decimal, which can be broken into two parts:

• The whole number part is: 1.
• The decimal part is: 0.09.

We aim to convert the entire number into a fraction.

Step 2: Isolate the Decimal Part (0.09)

Focus on the decimal part (0.09) and represent it as a fraction.

Step 2.1: Write 0.09 as \( \frac9100 \)

The decimal 0.09 can be read as "9 hundredths." Mathematically, this is:

\[ 0.09 = \frac9100 \]

Step 2.2: Simplify the Fraction

Now simplify \( \frac9100 \) by finding the greatest common divisor (GCD) of 9 and 100.

• The GCD of 9 and 100 is: 1.
• Therefore, the simplified fraction is:

\[ \frac9100 \]

Step 3: Combine the Whole Number and Fraction

The original number 1.09 is the sum of the whole number 1 and the fraction \( \frac9100 \).

Combine these as a mixed number:

\[ 1.09 = 1 + \frac9100 = \frac109/100 \]

Step 4: Verify the Answer

To verify, divide \( \frac109/100 \):

\[ \frac109/100 = 1.09 \]

Thus, the fraction is correct.

Final Answer

The decimal 1.09 as a fraction is:

\[ \frac109/100 \]

If expressed as a mixed number:

\[ 1 9/100 \]