Step-by-Step Solution for Converting 1.66 to a Fraction

Step 1: Understand the Number

The number 1.66 is a decimal, which can be broken into two parts:

• The whole number part is: 1.
• The decimal part is: 0.66.

We aim to convert the entire number into a fraction.

Step 2: Isolate the Decimal Part (0.66)

Focus on the decimal part (0.66) and represent it as a fraction.

Step 2.1: Write 0.66 as \( \frac66100 \)

The decimal 0.66 can be read as "66 hundredths." Mathematically, this is:

\[ 0.66 = \frac66100 \]

Step 2.2: Simplify the Fraction

Now simplify \( \frac66100 \) by finding the greatest common divisor (GCD) of 66 and 100.

• The GCD of 66 and 100 is: 2.
• Therefore, the simplified fraction is:

\[ \frac3350 \]

Step 3: Combine the Whole Number and Fraction

The original number 1.66 is the sum of the whole number 1 and the fraction \( \frac3350 \).

Combine these as a mixed number:

\[ 1.66 = 1 + \frac3350 = \frac83/50 \]

Step 4: Verify the Answer

To verify, divide \( \frac83/50 \):

\[ \frac83/50 = 1.66 \]

Thus, the fraction is correct.

Final Answer

The decimal 1.66 as a fraction is:

\[ \frac83/50 \]

If expressed as a mixed number:

\[ 1 33/50 \]